Technical Comments

Response to Comment on "Grain Boundary-Mediated Plasticity in Nanocrystalline Nickel"

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Science  15 Apr 2005:
Vol. 308, Issue 5720, pp. 356
DOI: 10.1126/science.1107389

Our study (1) reported on the deformation response of nanocrystalline Ni during in situ dark-field transmission electron microscopy (DFTEM) straining experiments and showed what we view as direct and compelling evidence of grain boundary-mediated plasticity. Based on their analysis of the limited experimental data we presented, however, Chen and Yan (2) propose that the reported contrast changes more likely resulted from grain growth caused by electron irradiation and applied stress rather than from plastic deformation. Here, we give specific reasons why their assertions are incorrect and discuss how the measurement approaches they have used are inappropriate. Additionally, we present further evidence that supports our original conclusions.

The method Chen and Yan employed to measure displacement merely probes the in-plane (two-dimensional) components of incremental strain occurring during the very short time interval shown [figure 3 in (1)] instead of the accumulated strain. As we noted explicitly in the supporting online material in (1), the loading was applied by pulsing the displacement manually. After each small displacement pulse, the monitored area always moved significantly within or even out of the field of view. Clear images could be obtained only when the sample position stabilized within the field of view, and at that time severe deformation was nearly complete. Thus, little incremental strain occurs during this short image sequence [figure 3 in (1)], as one might expect.

We believe that the images shown in figure 3 of (1) are particularly valuable in understanding deformation in nanocrystalline materials. In general, the formation process of grain agglomerates simply occurred too fast to be recorded clearly. Moreover, instead of remaining constant after formation, the sizes of the grain agglomerates changed in a rather irregular manner in responding to the deformation and fracture process (see, for example, Fig. 1, B to D). This indicates that strong grain boundary-related activity occurred inside the grain agglomerates. Figure 3 in (1), a short (0.5 s) extract from more than 6 hours of videotaped experimentation (imaged ahead of cracks), not only reveals the formation process of a grain agglomerate, but also shows conclusive evidence for grain rotation and excludes the effect of overall sample rotation.

Fig. 1.

Dark-field TEM images showing deformation and fracture of nanocrystalline Ni in response to an applied tensile displacement pulse. Note the growth of larger grain agglomerates along the propagating crack path. Inset in (A) is an image from an undeformed area that has been prethinned with low-temperature ion thinning to show more clearly the presence of small grains as well as the narrow grain size distribution.

It should be noted that other small grains still exhibit some minor contrast changes in figure 3 in (1). Hence, using them as reference points yields measurements that may not be accurate to ±1 nm [as Chen and Yan (2) claim in their analysis] and limits the accuracy of their conclusions. Chen and Yan also claim that no deformation has occurred, yet simultaneously state that the analysis has a deformation measurement error of 0.5%. This is simply not consistent; even small strains of this order may cause plastic deformation.

In contrast with previous in situ TEM experiments (3-5), the special sample design adopted in our investigation (1) ensured that all deformation was primarily concentrated in a bandlike area ahead of the propagating crack. We found that these grain agglomerates were observed only in this bandlike thinning area as a response to the applied loads (Fig. 1B). No similar phenomena were detected under the electron beam alone or in stressed areas apart from the main deformation area, and these phenomena have not been reported during in situ observations of this same material made by other researchers (5). Subsequent cracks were always observed to follow this deformation area upon further displacement pulses (Fig. 1, C and D). This clearly indicates that the enlarged agglomerates do not result simply from electron irradiation plus stress, but rather from stress-induced deformation.

In their comment, Chen and Yan claimed a linear relation between “grain” area and time based on their measurements made from figure 3 in (1) and claimed that these measurements are exactly consistent with the classical grain growth equation. However, as we noted (1), the growth in size of this agglomerate is not isotropic and occurs in an irregular manner. For example, after bright contrast emerged from a grain about 6 nm in diameter, it remained well defined in size as a single, approximately equiaxed grain until t = 0.1 s (fig. S1). We have reproduced the “grain growth” plot of Chen and Yan (Fig. 2) using our entire video image sequence (fig. S1). Clearly, the growth in area of the agglomerate is not consistent with linear grain growth. (Unfortunately, only a portion of these data could be included in the original paper for reasons of space.) Notably, Chen and Yan did not apply a similar “grain growth” analysis to nearby grains; this would have yielded no information in support of their argument, as those grains show essentially no growth.

Fig. 2.

Changes in the area of the grain agglomerate as a function of time. Clearly, the growth in area of the agglomerate is not consistent with linear grain growth. Note the “terraces” indicated by black arrows, which suggest an “incubation” time between grain rotations.

In addition, if classical grain growth were occurring during our observations—even though it is not expected at ambient temperature in nanocrystalline nickel (6, 7)—the initial displacement pulse might have added mechanical driving force to overcome an apparent activation barrier that exists for the thermally activated process of grain growth. This additional mechanical contribution would diminish over time. However, once the appropriate larger grains would have grown to about 6 to 10 times the size of the average grain (see, for example, the large grains in figs. S1 and S2), their growth would be expected to continue at the expense of the smaller grains in their vicinity, because the curvature-derived driving force would be greater, more strongly favoring their continued growth and the reduction of the free energy of the material. However, this was not the case [see, for example, fig. S2, which was extracted immediately after the sequence shown in figure 3 in (1)]. Without any further displacement pulses, the key grain agglomerate stopped growing and then appeared to split with time. Further loading leads to crack propagation in the bandlike deformation area in an inter- or intra-agglomerate manner. Again using the nearby features as references, this subsequent splitting is further conclusive evidence of grain boundary-mediated plasticity and argues against classical grain growth.

The image shown as figure 2E in (1) allowed us to state that grain agglomerates, instead of individual large grains, resulted from the applied displacement pulse. To directly compare the undeformed and deformed states, the two diffraction patterns that appeared in our paper [figure 2, B and D, in (1)] were taken under identical conditions—that is, using the same illumination intensity, the same selected-area aperture size, and the same exposure time. Simply boosting the contrast, as Chen and Yan have done, fundamentally alters the information in these patterns and thus yields an inaccurate conclusion. Presumably they have mistakenly chosen to alter the images out of concern over whether we had taken them in an equivalent manner; unfortunately, their alteration of contrast removes the difference in background intensity, which demonstrates that the material has also thinned and thus has been plastically deformed.

When considering how DFTEM images are formed, it is clear that the smaller grains in the agglomerates exhibit essentially edge-on orientations of their {111} lattice planes, their {200} lattice planes, or both (1). From a thermodynamic view, it is very possible that these grains are divided by small-angle grain boundaries (which would consist of dislocation arrays) or even that some coalescence occurred (8). However, considering that grain agglomerates, after being formed, change their sizes in a rather irregular way in response to the deformation (for example, Fig. 1, B to D), classical grain rotation-induced grain growth, if it exists, is not likely to be prominent.

The contrast-inverting method used by Chen and Yan (2) on figure 2E in (1) is poorly chosen. A bright-field image is formed by selecting the direct beam in the selected-area diffraction pattern, which will include contrast information from all diffracting lattice planes. Alternatively, a dark-field image of the type we have used is formed by selecting a small part of the diffraction rings (for polycrystalline materials) using the objective lens aperture. The dark-field image only includes the contrast information from those grains that are oriented such that they contribute to the specific diffraction vectors (direction and length) contained in the small region of the diffracting rings that is selected by the objective lens aperture. Therefore, to obtain bright-field contrast by inverting the dark-field contrast is simply incorrect; bright-field and dark-field TEM images give strictly inverse intensity only when considering a two-beam diffraction condition in the kinematic electron diffraction limit (9). Moreover, diffraction-contrast TEM images display true grain sizes only when the diffraction condition, exposure time, and image intensities are selected correctly. Manipulation of TEM images by software is easy but is fraught with scientific peril and should be done only with great care.

In sum, it is unfortunate that only part of the video frames from our experiments could be included in (1), as this omission led to the incorrect deduction by Chen and Yan (2) of a false linear grain growth by subsequent measurements. However, the remaining supporting evidence that they present stems largely from inappropriate image contrast adjustments and a misreading of our original paper.

Supporting Online Material

Fig. S1 and S2

References and Notes

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