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6.1. Introduction Electrodeposited metals will nearly always possess some level of internal stress, even when no external load has been applied and dislocation densities are negligible. As a result, these types of stresses are often referred to as “intrinsic stresses”. Internal stresses can be measured on both a microscopic and macroscopic scale. Microstresses are determined based on measureable non-uniform strain (i.e., microstrain) in the material [Cullity and Stock (2001)]. This microstrain is measured from XRD line broadening caused by atomic scale defects [Macherauch and Kloos (1987)]. Earlier reports on measurements of microstrain in nanocrystalline materials have led to the conclusion that there is a strong relationship with grain size [e.g., Eckert et al. (1992), Weissmuller et al. (1995), Eastman et al. (1995), Sanders et al. (1995), Sun et al. (1996), Malow and Koch (1997), Zhao et al. (2001), Li and Ebrahimi (2003), Mishra et al. (2004), Derlet et al. (2005), Qin and Szpunar (2005), and Biju et al.

(2008)]. In this study, a systematic approach on the effect of grain size on microstrain is presented for the series of electrodeposited nanocrystalline Ni and Ni-Fe alloy samples.

Macrostresses are determined by measuring strain based on XRD line shifts [Macherauch and Kloos (1987)] which are representative of detectable uniform strain [Cullity and Stock (2001)]. Macrostresses in nanocrystalline materials have been reported on many occasions; however, there are only a few experimental studies which provide some insight into the underlying relationship with grain size [e.g., Czerwinski (1996), El-Sherik et al. (2005), Shamsutdinov et al. (2007)]. Additionally, there are only a few macrostress

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measurements using X-ray diffraction (XRD) on nanocrystalline materials, e.g., Sanders et al.

(1995), El-Sherik et al. (2005). In particular, the study on nanocystalline Ni by El-Sherik et al. (2005) demonstrated a significant difference in macrostress values when a polycrystalline sample having a ~5000 nm grain size was compared to a nanocrystalline sample having a grain size of 10 nm. As a result, it was suggested that this stress could be related to the grain size. In order to elaborate on this observation, a similar systematic approach on the effect of grain size on macrostresses is also presented for the series of electrodeposited nanocrystalline Ni and Ni-Fe alloy samples. The main objective of this study was to develop a relationship with internal stresses based on the microstructural characteristics of these materials identified in Chapter 4.

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6.2.1. Results Microstrain is measured based on XRD line broadening [Withers and Bhadeshia (2001)] due to inhomogeneous or non-uniform strain acting over submicroscopic areas, i.e., several atomic distances within a grain [Macherauch and Kloos (1987), Cullity and Stock (2001)]. The microstrain for the series of nanocrystalline Ni and Ni-Fe alloys was analyzed from XRD patterns using the accompanying software package as described in Chapter 3 (Section The respective microstrain values for the series of nanocrystalline Ni and Ni-Fe alloy samples are presented in Table 6.1. For discussion purposes, the growth fault probabilities from Chapter 4 (Section 4.5.4) are also included in Table 6.1.


The key findings presented in this section were previously published in the following refereed journal article:

J.D. Giallonardo, G. Avramovic-Cingara, G. Palumbo and U. Erb, “Microstrain and growth fault structures in electrodeposited nanocrystalline Ni and Ni-Fe alloys”, Journal of Materials Science, 48 (2013) 6689.

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6.2.2. Effect of Grain Size on Microstrain Fig. 6.1 presents a plot of microstrain as a function of grain size. Also included in the plot are the results of other studies on materials produced using electrodeposition synthesis techniques. As seen in Fig. 6.1, there is a distinct trend whereby microstrain tends to increase with decreasing grain size. A best fit (dashed) line is provided for the current data set. The best fit line was determined based on an inverse grain size relationship with microstrain [Weissmuller et al. (1995), Malow and Koch (1997)]. This inverse grain size relationship with microstrain was found to be in relatively good agreement with the data in the present study. To further illustrate the effect of grain size, we also consider the increasing microstrain trend with the corresponding increase in the intercrystal volume fraction (grain boundaries and triple junctions). The intercrystal volume fraction, f ic, as a function of grain size, d, are related based on Eq. 2-1[Palumbo et al. (1990)].

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0.3 0.2 0.2 0.1 0.1

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As grain size decreases, the intercrystal volume fraction in the material increases very rapidly for grain sizes less than 20 nm given by the solid line in Fig. 6.1. The best fit curve for the data (dashed line) in the present study tends to follow a similar increasing trend with intercrystal volume fraction (solid line). This is consistent with the notion that an increased presence of grain boundaries and triple junctions induces lattice strain which results in XRD line broadening [Qin and Szpunar (2005), Stukowski et al. (2009)].

The microstrain values obtained for the nanocrystalline Ni samples are in relatively good agreement with other studies on materials synthesized using the electrodeposition technique. For example, Mishra et al. (2004) reported values which agree very well with the

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current results, e.g., 0.25% for electrodeposited nanocrystalline Ni with a grain size of 22 nm, using the Williamson-Hall method described by Suryanarayana and Norton (1998). On the other hand, some differences for the nanocrystalline Ni-Fe microstrain values were observed when compared to results of Li and Ebrahimi (2003). In their study, single peak analysis was used to determine the microstrain which resulted in some higher and lower values when compared to the current study where the grain size and Fe concentration were similar. Thus, it is worth noting that there can be some dependence on the specific plating parameters used to synthesize the materials and the method used to analyze the XRD patterns when determining microstrain values. However, the general trend with grain size is consistent.

The rather significant microstrain which is present in nanocrystalline materials has often been associated with grain size [e.g., Eckert et al. (1992), Weissmuller et al. (1995), Eastman et al. (1995), Sanders et al. (1995), Sun et al. (1996), Malow and Koch (1997), Zhao et al. (2001), Li and Ebrahimi (2003), Mishra et al. (2004), Derlet et al. (2005), Qin and Szpunar (2005), Stukowski et al. (2009)]. This grain size effect has been linked to the HRTEM observations of localized strains at grain boundaries [Wunderlich et al. (1990), Ping et al. (1995), Li et al. (2000), Valiev et al. (2000)] which are similar to the observations made in Chapter 4 (Section 4.4.2) and proposed to be a result of mainly the local elastic deformation near grain boundaries that is necessary for joining of the crystals [Valiev et al. (1986)]. The quantitative model of Qin and Szpunar (2005) describes the dependence of microstrain on grain size and is based on these physical observations which is essentially a stress field brought on by localized strain at grain boundaries. The origin of the localized strain is thought to be a result of excess free volume (vacancies and vacancy clusters) in the grain

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boundaries Qin and Szpunar (2005). However, as mentioned earlier, electrodeposited metals possess excess free volumes in the grain boundaries with sizes smaller than a vacancy in a perfect lattice Zhou et al. (2009). Thus, the local strain present at grain boundaries resulting from the crystal joining process in these nanocrystalline materials is considered to be the dominant source.

In a closer examination of the current experimental data points in Fig. 6.1, there is some notable variability when compared to the best fit curve (dashed line). Similar observations have also been made in some of the experimental data from the previous studies.

Given these observations, a further investigation was carried out to identify the possible causes. In addition to the presence of a significant volume fraction of intercrystal defects (i.e., grain boundaries and triple junctions) in these materials, a contribution of other atomic scale defects resulting in microstrain induced XRD line broadening are considered. Based on the defects analysis carried out earlier, particular emphasis was placed on the possible effects of growth faults since they are known to contribute to microstrain induced XRD line broadening [Paterson (1952)].

When comparing the microstrain values of the pure nanocrystalline Ni samples and the nanocrystalline Ni-Fe samples with respect to grain size, there are some differences that result in the mentioned variability with the best fit curve (dashed line) in Fig. 6.1. In order to elucidate any potential effect of alloying, a plot of microstrain versus Fe concentration is presented in Fig. 6.2. In this plot, there is an increasing trend with the addition of Fe which

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suggests the presence of an alloying effect in addition to the effect of grain size. When considering their relative microstrain values and grain sizes, the samples containing Fe are consistently higher than the Ni samples. For example, sample no. 6 (Ni-7.3wt.%Fe, 32 nm) has a microstrain value which is noticeably higher than that of sample no. 5 (Ni, 23 nm). In this case, it would have been expected that the smaller grain size sample, i.e., sample no. 5 (Ni, 23 nm), would have the higher microstrain value. Another possible alloying effect can also be seen for samples no. 8 (Ni-23wt.%Fe, 10 nm) and 9 (Ni-32wt.%Fe, 10 nm), whereby each has practically the same grain size but the microstrain for the sample with a higher concentration of Fe, i.e., sample no. 9 (Ni-32wt.%Fe., 10 nm), is greater by about 15%. In the study carried out by Li and Ebrahimi (2003) on a series of nanocrystalline Ni-Fe alloys, the expected grain size dependence for samples containing similar Fe concentrations was

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observed. However, where the grain sizes of samples were similar and the Fe concentration increased, the microstrain also increased. Based on this observation, it was suggested to consider other possible contributions to microstrain induced XRD line broadening other than grain size [Li and Ebrahimi (2003)].

6.2.3. Effect of Growth Faults on Microstrain In Chapter 4, the presence of growth faults was identified qualitatively through HRTEM image analysis (Section 4.4.2) and quantitatively by determining growth fault probabilities using XRD pattern analysis (Section 4.5.4). Growth faults are known to contribute to microstrain induced (asymmetric) XRD line broadening [Paterson (1952)].

Growth fault probabilities in the nanocrystalline Ni samples were found to be relatively low.

This was consistent with the low occurrence of growth faults observed in the HR-TEM image analysis. In the case of the nanocrystalline Ni-Fe samples, the growth fault probabilities increased significantly with increasing Fe. This was also consistent with the high occurrence of growth faults observed in the HR-TEM image analysis.

The increased presence of growth faults supports the typically higher microstrain values noted in the previous section for the Fe containing samples, e.g., when comparing samples no. 5 (Ni, 23 nm) and 6 (Ni-7.3wt%Fe, 32 nm). In addition to this, sample no. 9 (Ni-32wt.%Fe, 10 nm) has a higher microstrain value when compared to sample no. 8 (Niwt.%Fe, 10 nm) although they have the same grain size. This is considered to be a result of the increased presence in growth faults due to the effect of increasing Fe on the stacking fault energy. For the nanocrystalline Ni-Fe alloys, it may be concluded that, in addition to a

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grain size effect, there is a contributing alloying effect on microstrain induced XRD line broadening due to the increased presence of growth faults with increasing Fe concentration.

6.3. Macrostress 6.3.1. Results Macrostresses are determined by detecting XRD line shifts [Withers and Bhadeshia (2001)] resulting from homogeneous or uniform strains acting over large areas, i.e., many grains [Macherauch and Kloos (1987), Cullity and Stock (2001)]. The XRD line shifts correspond to a change in interplanar spacing or lattice parameter. The 2D-XRD method used in this study effectively detects distortions of the diffraction cones which are analogous to detecting XRD line shifts using the conventional sin 2  method. The result of the analysis in both cases is a strain value. In the current study, the (311) ring was analyzed for all samples and the planar component macrostresses,  11 and  22, and the shear stress component,  12 values (Eq. 3-27) were determined. Macrostress determinations were carried out as described in Chapter 3 (Section 3.7) using 2D-XRD.

The samples were analyzed in the “as-deposited” state, having not undergone any surface treatments and/or plastic deformation. An example of the (220), (311), (222) and (400) 2D-XRD diffraction rings on the output screen of the GADDS software for sample no.

4 (Ni, 37 nm) is shown in Fig. 6.3. Shown in Fig. 6.4 is an example of the GADDS software performing an integration of the region along the  (or  ) direction which corresponds to tracing of the ring along the vertical axis of the image. The 2 value at a given hkl peak

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(400) (220) (311)(222) Figure 6.3. GADDS software output image of diffractions rings for sample no. 4 (Ni, 37 nm) showing the (220), (311), (222), and (400) diffraction rings.

Figure 6.4.

GADD software output image of integration along the (311) ring during stress analysis for sample no. 4 (Ni, 37 nm). Embedded within the image is the peak intensity profile as a function of 2 for the example region that is integrated.

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