«STRUCTURE AND PROPERTIES OF ELECTRODEPOSITED NANOCRYSTALLINE NI AND NI-FE ALLOY CONTINUOUS FOILS by Jason Derek Giallonardo A thesis submitted in ...»
4.5.2. Texture The orientation index, I hkl, is a measure of the relative intensity of each of the characteristic lines as compared to a randomly oriented nickel powder standard [Willson and Rogers (1964)]. The fractional intensities of the first four lines corresponding to the principal crystallographic directions for the samples were divided by the corresponding fractional intensities of the standard (Table 4.3) to obtain the orientation index for each diffraction line. The orientation indices were calculated using the method of Willson and Rogers (1964) described in Chapter 3 (Eq. 3-10) employing the XRD patterns generated for each of the samples. Table 4.5 presents the orientation indices for the four principal crystallographic directions.
The materials used in this study typically have dominant (111) and (200) peaks that are similar to previous X-ray diffraction patterns presented for Ni and Ni-Fe alloy electrodeposits [El-Sherik and Erb (1995), Cheung et al. (1995)]. The only exception is sample no. 3 whose (220) and (311) peaks are relatively significant in intensity.
Electrodeposited nanocrystalline materials are known to have fibre textures [McMahon and Erb (1989), Czerwinski et al. (1997)]. In this particular case, it may be said that samples no.
1, 2, 4, 6, 7, 8 and 9 have a strong (200) fibre texture. Sample no. 3 has a weak (200) fibre
texture and is closest to the random orientation relative to the other samples based on the orientation indices for the (220) and (311) peaks. Sample no. 5 has a weak (111)(200) double-fibre texture.
4.5.3. Grain Size The grain size was estimated by using the Scherrer formula (Eq. 3-13) and the FWHM of the (111) and (200) broadened lines. The results are summarized in Table 4.6.
Immediately, it can be seen that the grain size estimations resulting from the (111) broadened lines are consistently greater than those resulting from the (200) broadened line. Since XRD is an indirect method, grain sizes determined by imaging techniques, such as TEM, are often considered to be more reliable. A plot of XRD grain size vs. the TEM grain size is presented in Fig. 4.29 to assess the grain size difference for the two methods.
Plot of XRD grain size estimations vs. TEM grain size determinations. The reference (dashed) line represents a 1:1 agreement between the two methods.
The dashed line in Fig. 4.29 represents the agreement between the two methods. As seen in Fig. 4.29, the agreement between the XRD and TEM grain size estimations is good for those samples with grain sizes less than 20 nm. In fact, for these samples the TEM grain sizes are bound by the (111) and (200) estimations. According to the earlier analysis, the grain size distribution for these samples (no. 7-9) is log-normal and the grain volume distribution is relatively narrow. When TEM grain sizes are greater than 20 nm, the XRD grain size estimations tend to be considerably lower.
The use of XRD analysis to predict the grain size of materials with a broad grain size distribution that includes coarse grains (i.e., greater than 100-300 nm) is typically inaccurate.
This results from the fact that the coarse grains do not affect line broadening [Klug and Alexander (1974)] leading to the inability of XRD analysis to determine accurately the grain size of such materials [He et al. (2004)]. For the current study, evidence of broader grain size distributions are typically observed at average grain sizes greater than 20 nm which results in the underestimations. It is at this transition point where the XRD grain size begins to significantly disagree with the grain sizes determined via TEM image analysis. Thus, XRD grain size estimations are more accurate when the average grain size is less than 20 nm, and the grain size distributions are much narrower.
It should be noted that grain size estimations from XRD line width measurements (e.g., using Eq. 3-13) typically give volume-weighted “column lengths”. In order to reconcile this, the XRD volume-weighted “column length” must be compensated to yield an average grain diameter. Although TEM is normally used to verify the accuracy of
estimations provided by XRD methods, it should also be recognized that this analysis can produce notable uncertainty when considering the fact that the number of grains that can be analyzed is normally small in comparison with the rest of the sample. In addition to this, TEM image analysis is carried out based on the assumption that grains are approximately equiaxed [Krill and Birringer (1998)].
4.5.4. Growth Faults 184.108.40.206. Probabilities* The results of the HR-TEM analysis earlier identified the presence of lattice defects which are considered to be growth faults since no external loads were applied on the samples.
Based on this, a further analysis was carried out to quantify the growth fault probabilities in the series of electrodeposited nanocrystalline Ni and Ni-Fe alloys. Quantification of growth faults was performed by analyzing (111) and (200) peak asymmetries from the XRD patterns of each sample to determine their respective growth fault probabilities using Eq. 3-18 [Cohen and Wagner (1962)]. Note that the stacking fault probability is often considered to be inversely proportional to the stacking fault energy at constant dislocation density [Charnock and Nutting (1967)]. Table 4.7 presents the respective growth fault probabilities for each of the samples.
The growth fault probabilities for the nanocrystalline Ni samples were found to be relatively low. In other words, the relatively high stacking fault energy for pure Ni (120-130 *
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.
1.5 1.0 0.5
Plot of growth fault probability vs. Fe concentration in the deposit showing an increasing trend with increasing Fe. The dashed line is a (linear) best fit for the current data.
mJ/m2 [Carter and Holmes (1977)]) is consistent with the relatively low growth fault probabilities determined for the pure nanocrystalline Ni samples. This is also 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 significantly increased with increasing Fe. Fig. 4.30 shows a plot of the growth fault probabilities versus Fe concentration. This increasing trend with Fe is similar to that of Sambongi (1965) who noticed that the addition of Fe to conventional polycrystalline Ni increased the deformation stacking fault probability which reached a maximum near 50 wt.% Fe. More recently, Ni and Zhang (2012) demonstrated the effects of Fe concentration on the mechanical behaviour of nanocrystalline Ni-Fe alloys and noted an increasing compound (deformation and growth) fault probability with increasing Fe after rolling.
As mentioned earlier, the addition of soluble alloying elements in fcc metals is known to decrease the stacking fault energy [Murr (1975)], including Ni alloys [Nie et al. (1995)].
In the case of fcc Ni-Fe alloys, the addition of Fe to conventional polycrystalline Ni decreases the stacking fault energy almost linearly down to a minimum value at around 65wt.%Fe. For example, at 10, 20 and 30wt.%Fe, the stacking fault energies are approximately 103, 89 and 73 mJ/m2, respectively [Charnock and Nutting (1967)].
Similarly, as seen in Fig. 4.30, the growth fault probabilities increase more or less in a linear manner with increasing Fe concentration in the deposit. This observation provides evidence to support the earlier HR-TEM image analysis which showed an increased presence of growth faults with increasing Fe concentration.
220.127.116.11. Electron Structure The electron structure of alloys has often been recognized as having a controlling influence on the physical properties of solid solutions [Hume-Rothery and Raynor (1983)].
The controlling factor is referred to as the electron concentration which is typically expressed as the free-electron-to-atom ratio, e / a. The e / a ratio can be calculated in the following manner,
where, x is the atomic fraction solute content, and V Vsolute Vsolvent is the difference in valency of the solute and solvent atoms, respectively. The theory assumes that an alloy forms a crystal structure which accommodates the valence electrons with the lowest free energy. Several studies have shown that the there is a clear decreasing trend for stacking fault energy with an increase in the e / a ratio [Howie (1961), Thornton et al. (1962), Murr (1975)]. Wang (2004) employed this theory to describe the dependency of the e / a ratio on the stacking fault energy of various Cu alloys as it relates to cyclic deformation response and the transition of wavy-slip mode to planar-slip mode. When the stacking fault energies for polycrystalline Cu-Al, Cu-Zn and Cu-Mn fcc alloys are plotted as a function of the e / a ratio, there is a clear decreasing trend down to a minimum value. In other words, as the e / a ratio increases, the slope of the curve decreases. In fact, the slope goes to zero or the trend effectively reaches a minimum stacking fault energy value.
A similar analysis for the current study was carried out to examine the dependency of the stacking fault energy on the e / a ratio. Using the stacking fault energy values of
Plot of stacking fault energy (SFE) and growth fault probabilities (GFP) vs. the free-electron-to-atom ratio ( e / a ) for the Ni and Ni-Fe alloys.
Charnock and Nutting (1967) for the entire range of Ni-Fe alloys a plot vs. the respective e / a ratio may be constructed (see Fig. 4.31). In order to apply the electron theory the two atoms used to form the alloy must have differing valences. The valency for Ni is taken to be
2. In the case of Fe, there are two valences: 2 and 3. Thus, to calculate e / a ratios, the valency for Fe is assumed to be 3.
Increasing e / a ratio for the Ni-Fe alloys is synonymous with increasing Fe in the alloy. The stacking fault energy for the Ni-Fe alloys decreases linearly and reaches a minimum value at approximately 65wt.%Fe which corresponds to an e / a ratio of approximately 1.66. The stacking fault energy then begins to increase in a linear manner with further additions of Fe or increasing e / a ratio. Note that near the minimum, the alloy
is transitioning from the fcc phase to the bcc phase with increasing Fe and the reason for the change in slope is, in fact, this phase transformation. Also plotted in Fig. 4.31 are the growth fault probabilities determined for the series of nanocrystalline Ni and Ni-Fe alloys produced in the current study. As previously described, the growth fault probabilities for the nanocrystalline Ni-Fe alloys as a function of Fe concentration behave in a similar manner as that of the stacking fault energies of their polycrystalline counterparts. That is, the growth fault probabilities and the stacking fault energies of both the nanocrystalline and polycrystalline alloys have an approximate linear dependence with Fe concentration.
Similarly, they both also have a linear dependence with respect to the e / a ratio. Since there is a defined relationship between the stacking fault energy or growth fault probability and the e / a ratio, it follows that the electron theory applies to the Ni-Fe alloys. This emphasizes the importance of the e / a ratio in controlling their various physical and other properties.
Thus, it can be said that the growth fault probability or stacking fault energy for the Ni-Fe alloys also depend on the e / a ratio instead of simply the nature and concentration of the solute [Tiwari and Ramanujan (2001)].
4.6. Thermal Analysis 4.6.1. Total Enthalpy (Stored Energy) The main defects found in fully dense, single phase nanocrystalline materials are intercrystal defects. For example, at a grain size of about 10 nm, approximately 27% of the volume consists of grain boundaries and triple junctions (see Fig. 2.4b). In conventional deformed polycrystalline materials, the release of stored energy during annealing is often a result of recovery, recrystallization, and grain growth. The recovery process is accompanied
by a reduction in dislocation density while the recrystallization process forms new strain-free grains. Finally, at sufficiently high temperatures grain growth will occur. In nanocrystalline materials, the release of energy is often based on the assumption that the presence of dislocations and other lattice defects is negligible. Thus, the energy released in these materials is almost exclusively the result of grain growth or decreasing the number of intercrystal defects in the system.
This energy release can be measured via calorimetric techniques and used to characterize the material’s total enthalpy, H total, or stored energy due to intercrystal defects by integrating anisothermal heat release curves. In this study, differential scanning calorimetry (DSC) was used to produce anisothermal anneal curves for all nine samples.
Only those anisothermal anneal curves which produced significant heat releases were analyzed, i.e., samples no. 4-9. Examples of the anisothermal anneal curves are given in Fig.
4.32 for sample no. 4 (Ni, 37 nm) and Fig. 4.33 for sample no. 9 (Ni-32wt.%Fe, 10 nm).
Table 4.8 summarizes the total enthalpy, H total, the peak temperature, Tp, and Curie temperature, Tc, values for all of the specimens along with the respective grain sizes determined using TEM image analysis.