The rate sensitivity and plastic deformation of nanocrystalline tantalum films at nanoscale
© Cao et al; licensee Springer. 2011
Received: 20 October 2010
Accepted: 1 March 2011
Published: 1 March 2011
Nanoindentation creep and loading rate change tests were employed to examine the rate sensitivity (m) and hardness of nanocrystalline tetragonal Ta films. Experimental results suggested that the m increased with the decrease of feature scale, such as grain size and indent depth. The magnitude of m is much less than the corresponding grain boundary (GB) sliding deformation with m of 0.5. Hardness softening behavior was observed for smaller grain size, which supports the GB sliding mechanism. The rate-controlling deformation was interpreted by the GB-mediated processes involving atomic diffusion and the generation of dislocation at GB.
Much research interest has been focused on uncovering the novel plastic deformation mechanisms of nanocrystalline (NC) metals over the last two decades [1–5]. As the average grain size (d) decreases to less than 100 nm, grain boundary (GB)-mediated processes, such as GB diffusion and sliding, become increasingly more important during plastic deformation . Molecular dynamic simulation , bubble raft model , and experimental results  suggested that the corresponding critical d of NC Cu and Ni for softening behavior is below 20 nm. In contrast, the other experimental observations suggest that the strength induced by dislocation activation still increases even if d decreases to 20 nm [7, 8]. So far, the dominant deformation mechanism of NC metals has not been clear yet.
Strain rate sensitivity (m) is an important dynamic parameter for understanding the plastic deformation of polycrystalline metals. In general, NC metals show a higher m than that of coarse grain (CG) and ultrafine grain (UFG) counterparts due to the enhanced GB-mediated process. For NC Cu of d ~ 10 nm, the value of m ~ 0.06 was ten times higher than that of CG Cu and single grain Cu . A higher m of 0.14 was reported for NC Cu with d ~ 26 nm produced by electric brush plating . NC Ni also exhibited a higher m than that of CG and UFG Ni during depth-sensing indentation and tensile testing . The increased m was attributed to GB mediated process instead of dislocation activation. In addition to d, it was found that the decreasing twin thickness could also increase the m of NC metals . In exceptional case, a negative m was observed for some nanostructured Al alloy which was caused by the interaction between dislocations and solutes . Recently, it was found that monometallic NC tetragonal Ta also exhibited negative m during indentation deformation . The main reason was believed to be the phase transformation underneath the indenter. However, the negative m of NC tetragonal Ta was not demonstrated further by subsequent research. In our previous study , a remarkable diffusion creep behavior has been revealed for NC tetragonal Ta at room temperature (RT). Nevertheless, the rate-controlling mechanism is still not clear. The aim of this study is to reveal the rate-controlling deformation mechanism of NC tetragonal Ta films by nanoindentation.
Ta films of two different d were deposited on Si (111) substrates in an inert environment of Ar gas by DC magnetron sputtering using a 99.95% pure Ta target. Before deposition, the Ta target was cleaned by sputtering Ar for 30 min. All the substrates were sequentially cleaned in an ultrasonic bath of acetone and alcohol. The base and working pressure of the chamber were kept at 6.0 × 10-5 and 1.4 Pa, respectively. The sputtering power was maintained at about 250 W. During deposition, the growth rate was 45 nm/min. By adjusting the total time of deposition, the thickness of the films was kept at about 2 μm. Different temperatures of the substrate at 300 K RT and 673 K were used for adjusting the grain size of Ta. The microstructure of Ta films was characterized by X-ray diffraction (XRD) using Cu Kα radiation source and transmission electron microscopy (TEM; JEM-2100).
Nanoindentation tests were performed at RT using a TriboIndenter from Hysitron Inc., Minneapolis, MN, USA, with a Berkovich diamond indenter with nominal tip having a radius of curvature R of 150 nm. Hence, the minimum depth for self-similar indentation was estimated to be 9 nm, which was calculated from the equation R(1 - sin 70.3°) = 0.06R . Displacement and load resolution of the instrument were 0.1 nm and 100 nN, respectively. The indentation depth (h) was controlled below 1/10 of the film thickness to eliminate the substrate effect. In order to ensure the credibility of the measurements, the drift measurement was performed immediately before testing. Then, the drift rate was calculated by linear regression of the displacement versus time during the drift analysis. The rate was used for correcting the indentation test data. For creep testing, the specimens were first loaded to a peak load (500-9000 μN) at a constant loading rate μN/s, and then the peak load was held constant for 40 s. Subsequently, the samples were unloaded to 10% of the maximum load and held at the same constant load for thermal drift correction. Apart from creep testing, the samples were measured with maximum load of 9800 μN at different constant loading rates ranging from 1 × 10-2 to 1 × 100/s without holding. Finally, the indenter was withdrawn to zero load. For consistent results, indentation tests at each load were repeated for at least ten times.
Results and discussion
Hardness versus strain rate is plotted in Figure 3. In both cases of d = 10 and 20 nm, the hardness increases with the enhanced loading rate. Moreover, all the plotted points of d = 10 nm show hardness lower than that of d = 20 nm in Ta film. It is suggested that a softening behavior occurs as d decreases to 10 nm. The loading rate sensitivity (m l) related to the thermally activation deformation behavior was examined by the definition of , where H and are the hardness and strain rate, respectively . The resultant m l of Ta films with d of 10 and 20 nm are 0.05 and 0.02, respectively. As a result, it is concluded that the magnitude of m l increases with the decrease of d.
It should be noted that the values of both m l and m c are positive, which is different from the negative m of NC tetragonal Ta as reported by Wang et al. . The negative m is attributed to β-α phase transformation underneath the indents. This negative m mainly occurs as the loading rate is below the 200 μN/s. However, in this research, most of the loading rates are higher than the 200 μN/s which may induce positive m. Grain refinement can often enhance m, especially when d decreases to nanoscale . The density of GB will significantly increase as d decreases to less than below 30 nm. The volume percentage of GB is estimated as GB vol% = 100% - (d - d GB)3/d 3, where the d GB is the thickness of GB . So far, it is a controversy question with respect to accurate determination the thickness of GB in NC metals. Ranganathan et al.  estimated that the GB region is only about 0.5 nm wide of the order of two to three lattice plane spacing, while the GB thickness of about 1 nm was reported by Meyers et al. . In ref. , it is suggested that the thickness of GB is about seven lattice parameters. Thus, the thickness of GB of tetragonal NC Ta was calculated to be about 3.7 nm. In this study, considering the three values calculated above, we selected an average value of about 2 nm as the thickness of GB for tetragonal NC Ta. Considering the value d GB = 2 nm, the volume percentages of GB at d of 10 and 20 nm are estimated to be about 48.8 and 27.1 vol%, respectively. The enhanced GB density usually advances GB-mediated process, such as Coble creep and GB sliding. However, both m l and m c are much lower than m = 0.5 expected for diffusion-controlled Coble creep, and m = 1 for GB sliding mechanism [28, 29]. Hence, GB diffusion and sliding are ruled out as dominant deformation for the present NC Ta films.
The dislocation-mediated mechanism is thus considered as the rate-controlling deformation process. It is well known that dislocation pile-up at GB is responsible for the grain refinement-induced hardening on CG and UFG metals, as they exhibit a normal Hall-Petch relation . However, the resultant hardness decreases as d decreases from 20 to 10 nm. Therefore, the dislocation pile-up process is also excluded as the dominant deformation mechanism. The reduction in hardness is due to d in support of GB-mediated process, while the low m l and m c relative to the Coble creep and GB sliding process with a higher m challenges the GB diffusion and sliding mechanism. It seems that there is an inconsistent conclusion obtained from the resultant hardness and the rate sensitivity. It has been documented that the transitional Frank-Read source inside the grain for dislocation nucleation and multiplication becomes invalid since the stress for their operation is inversely proportional to the size of the sources, as the d decreases to nano- and submicron-scale . Instead, the GB can be treated as the source of the dislocation emission and nucleation which was demonstrated by TEM observation and MD simulation [32, 33]. The dislocation emission is a rate-controlled process which could be thermally activated from GB as the dislocation activation is often associated with GB diffusion and shuffling of atom inside GB. One scenario is that the dislocation emitted from a GB, traveled through the entire grain, and wash eventually absorbed in the opposite GB . The other scenario is imagined to be that the dislocation bows out to a semicircle from the abundant GB source and injects a lattice dislocation at a relative low stress . Meanwhile, the crack-induced stress concentration was also in support of dislocation emission at a GB facet , which may also induce a low nucleation stress for GB dislocation. The enhanced GB process associated with dislocation activation may be responsible for reduced hardness with decreasing d. A model of "grain boundary-affected zone" at and near the GB was proposed to explain the enhanced rate sensitivity of NC Ni . The MD simulation indicates that the atoms at GB are easier to deform than that inside the grain for NC Cu and Ni [37, 38]. For the present NC Ta films, the volume percentage of the GB increases from 27.1 to 48.8 vol% as d decreases from 20 to 10 nm. In both cases, the volume percentage of the GB is much higher than that of the UFG/CG metals. Therefore, it is believed that the enhanced GB-mediated processes involving atomic diffusion and dislocation generation at GB are responsible for the decreased hardness and increased rate sensitivity with reduced d.
In summary, we have examined the rate sensitivity and hardness of NC tetragonal Ta films by indentation creep and loading rate change tests. It is suggested that m l and m c increase with the decrease of d and h, respectively, which exhibits a remarkable size effect. The hardness becomes smaller as d decreases from 20 to 10 nm. The Coble creep and GB sliding are excluded for dominant deformation mechanism. Instead, GB activation processes involving atomic diffusion and dislocation generation at GB are enhanced to mediate the plastic deformation process.
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transmission electron microscopy
The study presented in this article was jointly supported by the Ministry of Science and Technology of China (2010CB631004, 2009GJC10032), the Science and Technology Department of Jiangsu Province (BY2009148, BE2009139), the Natural Science Foundation of China (11004098, 50831004, 51001060), and the Open Project Program of Xiangtan University (KF0910). The authors also thank Mr. Syed Junaid Ali for his valuable help in improving the manuscript.
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