Effect of Annealing on Hardness and the Modulus of Elasticity in Bulk Nanocrystalline Nickel

The XRD profile of 20-nm as-received (ED) nc-Ni exhibited strongly preferred texture along the (200) planes (Figure 1). Similar results on (ED) nc-Ni have also been reported by several investigators.[17,26‐29] This texture was mainly attributed to presence of impurities in the electrolyte bath, namely S and C, which seem to enhance the strength of the (100) texture by reducing the (100) surface energy. The texture was also present in annealed samples (Figure 2). Below 500 K (227 °C), the preferred orientation along the (200) planes was still present when samples were annealed at 1 and 25 hours, although it diminished with an increasing annealing temperature. Above 500 K (227 °C), texture was lost and randomly oriented grains were detected, as demonstrated by representative EBSD orientation maps in Figure 8.

The XRD and TEM techniques have been frequently used to compare measurements of grain sizes. The results reported by several investigators[17,30‐32] indicated that the measurements obtained from both methods were comparable. However, recent studies[33‐35] have demonstrated that grain size measurements from XRD lead to underestimation when deviations in narrow grain size distributions occurred.

In the present study, it is shown that the grain size values of as-received (ED) nc-Ni samples measured by XRD and TEM were in excellent agreement, while the values obtained from annealed samples were not (Table II). It is suggested that under this condition, reliable results from XRD are not obtained for the following two reasons: (1) a bimodal distribution of the grain size with a wide grain size distribution exists after annealing at temperatures <500 K (227 °C) and (2) significant grain growth occurs after annealing at temperatures >500 K (227 °C) and, as a result, the values of grain sizes for a large number of grains in the microstructure exceed the limitation of XRD (100 nm). Similar observations were made by other investigators[31,33,35] who have reported that XRD is not a valid characterization technique for samples with an inhomogeneous distribution of grain size and for grain sizes >100 nm.

According to the present data, grain growth in (ED) nc-Ni exhibits the following two types of behavior depending on the annealing temperature: (1) below 500 K (227 °C), anomalous grain growth and bimodal grain size distributions were detected and (2) above 500 K (227 °C), there was normal grain growth. These types of behavior were noted earlier in bulk nc-Ni by Chauhan and Mohamed,[17] who have characterized each behavior with a different activation energy: a low activation energy of approximately 25 kJ/mol below 0.3 T _m and a high activation energy of approximately 125 kJ/mol above 0.3 T _m . The low activation energy was a characteristic of reordering boundaries for nc metals, while the high activation energy was close to the grain boundary diffusion activation energy value in polycrystalline Ni.

The present results reveal a major transition in the hardness behavior of nc-Ni at 500 K (227 °C) as a result of annealing (region III). In addition, according to Figure 6, the hardness of (ED) nc-Ni is almost constant below 350 K (77 °C) and for short holding annealing times (region I) and slightly increases with increasing annealing temperatures between 350 and 500 K (77 and 227 °C) (region II, hardening), while it decreases with increasing annealing temperatures above 500 K (227 °C) (region III, softening).

Softening above 500 K (227 °C) (region III) can be attributed to the occurrence of significant grain growth. For example, the initial grain size of 20 nm after annealing at 593 K (320 °C) grew to 240 nm. According to the conventional HP equation,[23,24] an increase in grain size leads to a decrease in hardness.

The origin of the occurrence of hardening in region II (350 K (77 °C) < T < 500 K (227 °C)) cannot be attributed to the reduction in porosity level, because the electrodeposition route produces a fully dense nc-Ni.[19] Accordingly, other possible explanations need to be sought. In the following paragraph, one possible explanation, which is based on the available information and the results of the present investigation, is offered.

Recent molecular dynamic simulation by Hasnaoui et al.[36] has suggested that grain boundaries of as-prepared nc materials are often in a nonequilibrium state after processing and that as a result of thermal annealing, the grain boundaries and triple-junction regions approach equilibrium. This process results in strengthening the material (hardening) and in reducing its ductility. The results of the computer simulation[36] are consistent with the experimental data reported by Wang et al.[8] for fully dense nc-Ni prepared by electrodeposition the grain size of which was approximately 15 nm. In this regard, the occurrence of region I, which exists at T < 350 K (77 °C) and in which the hardness remains essentially constant, can be attributed to the possibility that in the temperature range 300 to 350 K (27 to 77 °C), the kinetics are too slow to induce any changes in the nonequilibrium structure resulting from processing.

An examination of the TEM micrographs as exemplified in Figure 9 indicates the presence of twins in the large grains of the samples that were annealed at 443 K (170 °C) for 25 hours and 493 K (220 °C) for 1 hour and that showed a bimodal grain size distribution. Twins are also observed at temperatures >500 K (227 °C) during normal grain growth, as revealed by the EBSD orientation map in Figure 8, in which twins are identified as “T,” although their densities were lower than those noted at temperatures <500 K (227 °C). These twins were originated during the annealing process when deformation processes were not involved in the experimental procedure (only heat treatment was carried out). Thus, the induced twins are referred to as annealing twins.

It is documented that twins can serve as a source for strengthening in nc materials.[37,38] Deformation twins are observed in fcc metals and alloys with a low stacking fault energy. However, under severe deformation conditions in nc materials, twins have also been observed in metals with a higher stacking fault energy. The primary effects of the presence of twins are the following: (1) the grains are subdivided into smaller grains (the effective grain size becomes much smaller than that initially characterized by TEM) and (2) twin boundaries, like grain boundaries, can serve as barriers to dislocation motion. In this regard, it was shown that Cu conventional HP behavior was valid when the twin spacing was replaced by the grain size.[39]

In Figure 10, the values of hardness measured following annealing are plotted against the grain size. An examination of the figure indicates that the values of hardness are much higher than those predicted from conventional HP behavior for the measured grain sizes. In order to check whether the difference between experimental measurements and prediction may arise from the effect of the presence of annealing twins in the interiors of the grains, a number of representative TEM micrographs were used to estimate the effective grain size.[40] The values of effective grain sizes obtained as a result of the twinning correction (represented by triangles) along with those of the grain sizes prior to making the correction (represented by squares) are shown in Figure 10. It is clear that as a result of incorporating the effect of annealing twins, considerable improvement in the correlation between the experimental values of the hardness and the position of the line representing conventional HP behavior is achieved. Equally important is the finding that the average effective grain sizes in the region of hardening (low annealing temperatures) are slightly less than the initial grain size of 20 nm (Table III). This finding tends to explain in part the slightly high values measured for hardness at annealing temperatures lower than 500 K (227 °C), despite the occurrence of some grain growth.

The modulus of elasticity E of as-received (ED) nc-Ni was found to be 165 ± 10 GPa. This value can be compared with values for the modulus estimated from two sources. First, according to the Hill approximation[41] for averaging different grain size orientations, the E for coarse-grained Ni was estimated to be 213 GPa. Second, the upper and the lower bounds for E in polycrystalline Ni can be estimated here using the Voigt’s average and the Reuss average, respectively. The Voigt’s average for the modulus of elasticity is given by[42]where \( F = {\frac{1}{3}}\left( {C_{11} + C_{22} + C_{33} } \right),\,G = {\frac{1}{3}}\left( {C_{12} + C_{23} + C_{13} } \right), \) and \( H = {\frac{1}{3}}\left( {C_{44} + C_{55} + C_{66} } \right) \). The Reuss average for Young modulus is given by[41]where \( F^{\prime} = {\frac{1}{3}}\left( {S_{11} + S_{22} + S_{33} } \right),\,G^{\prime} = {\frac{1}{3}}\left( {S_{12} + S_{23} + S_{13} } \right), \) and \( H^{\prime} = {\frac{1}{3}}\left( {S_{44} + S_{55} + S_{66} } \right) \).

Under the condition of cubic symmetry, C ₁₁ = C ₂₂ = C ₃₃, C ₁₂ = C ₂₃ = C ₁₃, and C ₄₄ = C ₅₅ = C ₆₆ (the same characteristic applies to the elastic compliances S). Using the elastic compliances for monocrystalline nickel at ambient temperature (S ₁₁ = 0.734 × 10⁻², S ₁₂ = −0.274 × 10⁻², and S ₄₄ = 0.802 × 10⁻² GPa⁻¹) and the elastic stiffness[43,44] (C ₁₁ = 252.8, C ₁₂ = 152.0, and C ₄₄ = 123.8 GPa), E _v and E _R were calculated as ~240 and 200 GPa, respectively.[44] A comparison between the values of the modulus of elasticity obtained from the aforementioned sources and the value of the modulus of as-received nc-Ni shows clearly that the latter value is lower than the following: (1) the value based on the Hill approximation[41] and (2) the lower bound of E as defined by E _R.

According to the XRD profiles (Figure 1), a strong (200) texture was detected in the material. It is quite possible that this texture may be responsible for the reduced value of 165 GPa for the modulus of elasticity of the as-received nc-Ni. Three pieces of information lend support to this possibility. First, Fritz et al.[29] reported an E value of 165 GPa in nc-Ni that exhibited preferred orientation along the (100) planes. Second, as shown in Figure 7, the modulus increases continuously with the increasing annealing temperature, approaching a maximum plateau of approximately 240 GPa. This finding parallels in trend XRD profiles for annealed sample of nc-Ni, which show that the strong (200) texture continues to diminish with increasing annealing temperature. Third, the modulus of elasticity depends on the orientation of the material. In a cubic material such as Ni, the modulus of elasticity can be determined along any orientation using the following expression:[44]with \( F = lxx^{{\prime 2}} lyx^{{\prime 2}} + lyx^{{\prime 2}} lzx^{{\prime 2}} + lzx^{{\prime2}} lxx^{{\prime2}} \)where F is an orientation factor, lxx ′ is cosine the angle between x ′ and x, lyx ′ is cosine the angle between x ′ and y, and lzx ′ is cosine the angle between x ′ and z. Using the elastic compliances for monocrystalline nickel that were given earlier, E values at [100], [220], and [111] were calculated as ~140, 232, and 300 GPa, respectively. A comparison between these estimated values of E and the experimental value of 165 GPa (as-received nc-Ni) indicates that the preferred orientation along the (100) planes is most likely responsible for the reduced value of E measured for as-received nc-Ni. Finally, the texture along (200) is lost above 500 K (227 °C), as indicated by Figure 2(d), and grains become randomly oriented, as shown by EBSD orientation maps given in Figure 8. Under these conditions, E approaches a maximum value of approximately 240 GPa that is essentially equal to the Voigt’s average estimated above for polycrystalline Ni.