HighP–T Nano-Mechanics of Polycrystalline Nickel
© to the authors 2007
Received: 2 August 2007
Accepted: 4 September 2007
Published: 26 September 2007
We have conducted highP–T synchrotron X-ray and time-of-flight neutron diffraction experiments as well as indentation measurements to study equation of state, constitutive properties, and hardness of nanocrystalline and bulk nickel. Our lattice volume–pressure data present a clear evidence of elastic softening in nanocrystalline Ni as compared with the bulk nickel. We show that the enhanced overall compressibility of nanocrystalline Ni is a consequence of the higher compressibility of the surface shell of Ni nanocrystals, which supports the results of molecular dynamics simulation and a generalized model of a nanocrystal with expanded surface layer. The analytical methods we developed based on the peak-profile of diffraction data allow us to identify “micro/local” yield due to high stress concentration at the grain-to-grain contacts and “macro/bulk” yield due to deviatoric stress over the entire sample. The graphic approach of our strain/stress analyses can also reveal the corresponding yield strength, grain crushing/growth, work hardening/softening, and thermal relaxation under highP–T conditions, as well as the intrinsic residual/surface strains in the polycrystalline bulks. From micro-indentation measurements, we found that a low-temperature annealing (T < 0.4 Tm) hardens nanocrystalline Ni, leading to an inverse Hall–Petch relationship. We explain this abnormal Hall–Petch effect in terms of impurity segregation to the grain boundaries of the nanocrystalline Ni.
Nanocrystalline materials hold the promise of revolutionizing traditional materials design in many applications via atomic-level structural control to tailor technological properties. As opposed to the micron-scale, the nanoscale is not just another step towards miniaturization, but is a qualitatively new scale because this size constraint often produces qualitatively new behavior. It starts to become clear that when the crystal size and/or domain size become comparable with a specific physical length scale such as the mean free path, the dislocation dimension, the domain size in ferromagnets or ferroelectics, the coherence length of phonons, or the correlation length of a collective ground state like superconductivity, the corresponding physical phenomenon will be strongly affected. Extensive experimental studies over the past decade have shown that a variety of properties, such as phase stability , melting temperature , yield strength [3, 4], elastic modulus [5–8], and electronic structure , can strongly be altered as crystallite size decreases from micrometers to nanometers.
Nickel is a 3d transition metal of technological importance. Nanocrystalline nickel (nano-Ni) has been the subject of considerable experimental and theoretical work in recent years. The elastic, mechanical, magnetic, and electrical properties, as well as diffusion coefficients and vibrational modes of nano-Ni have been widely studied [10–15]. In order to understand better the nano-mechanics of polycrystalline Ni, particularly its behavior under elevated pressure and/or temperature, we have recently conducted a series of synchrotron X-ray and time-of-flight neutron diffraction experiments as well as indentation measurements to study its equation of state, constitutive properties, and hardness [4, 16–18]. To accurately characterize the unique properties of nano-Ni, we studied both nano and bulk Ni using identical techniques, and in some cases with the two metals investigated simultaneously in a single high P–T experiment for direct comparison. The experimental results are summarized in this review article.
Elastic Softening in Nanocrystalline Nickel Metals
Among many properties that have so far been investigated on nanocrystalline materials, the grain-size effect on the elastic properties is still a matter of controversy and has not been well understood. The Young’s modulus values of nanocrystalline materials obtained in early measurements, for example, have found to be substantially lower than those of their bulk counterparts . Even though this softening phenomenon can partly be attributed to the presence of a large volume fraction of pores and cracks in the as-prepared nanocrystalline materials, later measurements on porosity-free nanocrystalline samples as well as theoretical calculations [20–22] still revealed an elastic softening in materials with grain size smaller than 20 nm. Contrary to these findings, a number of recent compression studies using X-ray diffraction reported higher bulk modulus for nanocrystalline materials than for the regular polycrystals [5–8]. Furthermore, in some materials such as Fe, Ni, MgO, and CuO, the compressibility was found to be independent of the crystallite size [10, 11, 23, 24]. While there may not exist a universal law for the grain-size effect on the materials’ elastic properties, it is possible that conclusions from at least some of these studies are inconclusive or perhaps misleading. The reasons can be two folds. On one hand, many of these experimental studies were focused on nanocrystalline materials only, and, therefore, the comparison with early published data for conventional materials would be vulnerable to the systematic errors of the experiments using different techniques. On the other hand, this effect may be too subtle to be resolved with the experimental methods applied. We recently studied compressibility of nano- and micro-crystalline nickel in a single high-pressure experiment using synchrotron X-ray diffraction . This comparative approach would eliminate systematic errors arising from instrument response and pressure/deviatoric-stress determination and thus allows detection of small difference in compressibility measurements [25, 26].
The microcrystalline nickel powders were commercially obtained which are 99.8% pure and have a grain size distribution of 3–7 μm. The nanocrystalline powders used in this study were prepared by ball milling, starting from coarse-grained powders of Ni (<840 μm, 99.999%) supplied by Alfa Aesar (Ward Hill, Massachusetts). Five grams of powder were ball-milled for 30 h using a SPEX 8000 mill, hardened-steel vials, and 30 1-g hardened steel balls. The SEPX mill was operated inside an argon-filled glove box containing less than 1 ppm oxygen. Measurement of the Curie transition temperature by a Differential Scanning Calorimetry technique  suggests that the as-prepared nanocrystalline Ni contain approximately 1 at% Fe impurity. Based on the peak width analysis of X-ray diffraction at ambient conditions (see later discussion), the nanocrystalline powders have an average grain size of 12–13 nm. For both starting Ni powders, neutron diffraction at the Bragg angles of 40°, 90°, and 150° reveals no preferred orientation texture. The high-pressure X-ray diffraction experiment was performed using a cubic anvil apparatus  at beamline X17B2 of the National Synchrotron Light Source, Brookhaven National Laboratory. An energy-dispersive X-ray method was employed and the cell assembly used is similar to those described in the reference . The two Ni samples were placed in a boron nitride sleeve, separated by a layer of NaCl, which also serves as internal pressure standard. The pressure was determined using the Decker equation of state  for NaCl.
The compressibility of nanocrystalline Ni has recently been studied by X-ray diffraction in diamond anvil cells. Chen et al.  measured the variation of lattice volume with pressure up to 55 GPa and found that the bulk modulus of nanocrystalline Ni (K 0 = 185.4 ± 10 GPa) is similar to the value (K 0 = 180 GPa) previously reported for the bulk Ni. In another study of Rekhi et al. , the experimentally determined bulk modulus for nanocrystalline Ni (K 0 = 228 ± 15 GPa) was found to be comparable to that obtained from ab initio calculations of their own for the bulk Ni (K 0 = 217 GPa). Based on these results and in contrast to the findings of the present work, both studies concluded that there is no crystallite-size effect on the compressibility of Ni. This conclusion, however, should be viewed with some caution because systematic errors typically exist among measurements with different techniques (including theoretical calculations). The comparative approach of this work can practically eliminate pressure and deviatoric stress as variables and is particularly suitable for detection of subtle difference in compressibility measurements.
The enhanced compressibility in nanocrystalline Ni is consistent with the common view of a reduced atomic density and hence a general expectation of an increasing compressibility of interatomic spacings in the surface layer of nanocrystalline materials [19, 31]. However, there is essentially no information available on the specific arrangement of atoms at the surface of nanocrystals, and so far there exist no experimental methods that can directly distinguish the compressional behavior between the surface region and the crystalline cores. Nevertheless, based on a high-pressure Mössbauer spectroscopy study , a technique that can discriminate between the spectral components of the intercrystalline region and the crystalline core, Trapp et al. had deduced that the surface layer of nanocrystallie Fe has an enhanced compressibility when compared to the bulk crystalline α-Fe.
Recently, in a series of publications, Palosz and coworkers [32–34] showed that it is practically impossible to derive a single set of lattice parameters and hence a unique value of the overall bulk modulus from the positions of the Bragg reflections for nanocrystals. They proposed a methodology of the analysis of powder diffraction data for nanocrystals based on calculations of the lattice parameter values from individual Bragg reflections. Such quantities, which are associated with the specific values of the diffraction vectors Q (Q = 2π/d, where d is the d-spacing in the unit of Å) of the corresponding reflections, are termed as “apparent lattice parameters”, alp. Based on theoretical calculations of powder diffraction data for nanocrystals with strained surface shell as well as experimental data of nanocrystalline SiC, the alp values are found to exhibit a complex dependence on Q with some characteristic minima and maxima. Careful analysis of these features may shed light on the atomic structure and behavior of nanocrystals, particularly those of the surface shell. According to Palosz’s analysis, the reflections observed at very large Q could be used to probe the properties of the grain core (such as the real lattice parameter(s) of nanocrystals), whereas the reflections observed at small Q values are sensitive to the structure of the surface of the grains.
The grain-size dependence of the bulk modulus of nanocrystalline Ni has recently been investigated using molecular dynamics simulation . Similar to the present findings, the calculated P–V data for Ni nanocrystals revealed a decrease of the “overall” bulk modulus up to 7% when compared with that of the single crystal Ni. Using a simple mixture model where the bulk modulus of nanocrystals is the sum of the elastic responses from two structurally different components, the bulk modulus of the surface layer at 286 K is found to be 9.2% smaller than that of the crystalline grains, which is in qualitative agreement with the present finding. Therefore, both experiment and theoretical calculation show that the enhanced “overall” compressibility of nanocrystalline Ni is a consequence of the higher compressibility of the surface shell. Our study demonstrates that careful compressional experiments with powder diffraction can be a useful means for probing the structure and behavior of the surface layer in nanocrystalline materials.
HighP–T Constitutive Properties of Nano and Bulk Ni
Yield strength (σy) is an important constitutive property of materials to define the onset of plastic deformation and viscous flow and is conventionally determined from the stress–strain measurements for engineering materials. Recent advancements in diffraction techniques with high intensity synchrotron X-ray and time-of-flight neutron allow the deformation studies for the bulk samples at the atomistic level [3, 4, 36–39]. Based on the classic Williamson-Hall method and its subsequent variations [40–45], the strain/strength, dislocation density, and crystal size can be derived from the peak-width analysis of diffraction data. This method will also overcome the sample porosity or impurity problems commonly faced in the conventional indentation or deformation experiments. Generally speaking, the polycrystalline diffraction profile is a convolution function of instrument response, grain size distribution, and crystal lattice deformations along the diffraction vector. During high-pressure compression experiment, the breaths of diffraction peaks broaden, and the amount of peak broadening indicates the distribution of differential strains along the diffraction vector , which is typically owing to different crystalline orientations relative to the loading direction and particularly to the stress concentration at grain-to-grain contacts during the powder compaction. The diffraction peak widths reach the maximum as the deviatoric stress approaches the ultimate yield strength and the sample material begins to flow plastically. By applying a stress field on crystalline sample and monitoring the peak width variation of different hkl diffractions as a function of pressure, one can derive the differential strain, thus the constitutive properties of the sample materials. In high-temperature annealing experiments without applied external stress, diffraction peak width sharpens with increasing temperature, reflecting the relaxation of residual strain and, in the case of nanocrystalline materials, demonstrating both the surface strain release and grain growth.
By multiplying the DER2 to the observed raw data, we can correct the strain differences of individual lattice planes. As shown in Fig. 6, the corrected data (solid blue and dark cyan circles) can be readily fit to a straight line in the versus d 2 (P, T) plot and allow us to derive the apparent strain and grain size information unambiguously. From the (E hkl /E111) 2 and (E hkl /E200) 2 corrections, we effectively obtain the lower and upper bounds, respectively, for the apparent strains.
Loading–Unloading Loop and Energy Dissipations
The two-stage yielding phenomenon, however, is not as obvious in the nano-Ni, as it exhibits pronounced non-linear ductility. The “local” plastic deformation is expected to take place at pressures much lower than 0.4 GPa, which is difficult to determine with our experimental techniques. On the other hand, the work-hardening to higher strain is clearly observed for the nano-Ni. The nano-Ni also recovers a much larger fraction of the incurred strain upon unloading, 83–84%, depending on maximum pressure, whereas the micron-Ni only recovers 49–52%, respectively. The un-recoverable strain can be caused by intergranular (e.g. elastic and plastic anisotropy) and/or intragranular (e.g. heterogeneous stress distribution and dislocation density) mechanisms. Previous studies  have shown that nano-Ni show full recovery of dislocation density when loaded in uniaxial tension. Interestingly, we observe that the recoverability for the nickel samples remain about the same level for the unloading before and/or after the bulk yielding. This, and the combination of almost full recovery for nano-Ni and less recovery for the micron-Ni in our triaxial-stress experiments, suggests that the unrecoverable part of the plastic strain in the nano-Ni is due to intergranular strains (elastic and plastic anisotropy) whereas it is mainly intragranular strain (dislocation density), in the micron-Ni.
The loading–unloading hysteresis loop illustrated in Fig. 7 is more significant for the after-yield samples (right panel) than the before-yield samples (left panel), despite the comparable recoverability for both samples. The similar strain recoverability before- and after-yields indicates that the dislocation densities in nickel samples become saturated in the elastic loading stage and there is no further development in the plastic/ductile flow stage. The much large hysteresis loop for the micron-Ni after the yield suggests that the high-P works upon the micron-Ni are dissipated as heat, as we often experienced in the fatigue failure of nail bending. The dissipation loop is much smaller for the nano-Ni sample, indicating significantly reduced energy loss in its work-hardening plasticity deformation stage. The reduced level of energy dissipation for the nano-Ni during the loading-unloading cycle indicates that the nanostructured materials may be able to more readily endure greater mechanical fatigue in cyclic load path changes, a significant discovery of nano-mechanics.
Graphic Derivation of Thermo-Mechanics
The derived yield strength of high-P triaxial compression is for the nano-Ni, which is similar to the uniaxial tensile strength of 2.25 GPa determined by Budrovic et al. . The corresponding bulk yield strength (compression) of micron-Ni is , about a factor-of-three smaller than the nano-Ni. These observations are consistent with the classic Hall–Petch law [47, 48], which indicates a significant increase in materials strength as grain size decreases to the nanometer scale. The onset-pressure for bulk yielding in micron-Ni at is also smaller than for the nano-Ni at , Fig. 9, Left. In the plastic stage, continuous peak broadening indicates strain hardening, whereas peak sharpening indicates strain softening under certain high P–T conditions. There is an evident work-hardening for the nano-Ni, where the sample can still sustain higher differential/shear stress after the yielding, and another Δσnm ≈ +1.0 GPa is further loaded as the pressure increases to P = 7.4 GPa. However, the micron-Ni sample experiences a minor work softening at the high pressures.
It is well known that nano-metals have much less work hardening than the corresponding micron-metals in uniaxial tensile loading. Budrovic et al.  observed very limited strain-hardening in nano-Ni due to suppressed accumulation of dislocations after the plastic yielding. Our triaxial compression data shows opposite phenomenon, which may be because of pressure effects. It is unlikely from the artifacts due to plot of ε ap.-vs.-P (rather than conventional σ-vs.-ε), since the work-hardening/softening is observed in a comparative sense for the nano-/micron-samples under identical stress conditions.
As temperature increases, the stress variation in nano Ni exhibits two bending points, one at 600 K and the other near 1,000 K (Fig. 9, Right), dividing the stress-temperature variation into three different stages. Based on the grain size analysis, which will be discussed in the later part of the paper, the stress reduction atT = 300–600 K largely reflects the relaxation of both the applied/differential and surface/residual strains in the Ni nanocrystals, whereas atT = 600–1,000 K it is dominantly controlled by the grain growth. Since the stress-free state is reached at aboutT > 1,000 K, the initial surface/residual strains for the nano-Ni can be graphically determined as illustrated in the right panel of Fig. 9, which is 1.25 × 10−2and in excellent with the surface strain derived from neutron diffraction data at atmospheric pressure (see later discussion). It indicates the total removal of surface strain and annealing of apparent stress of about as the high-temperatures of 550 K < T < 1,150 K. For micron-Ni, the relaxation of apparent stress is not as vigorous as in the nano-Ni and a stress-free state is reached atT ≥ 800 K. Similarly, the residual stress exerted upon the starting (i.e., at ambient conditions) micron-Ni crystals can be graphically derived and is about .
The high temperature data in the final portion of the experiment atT > 1,100 K shows a complete merging of nano-Ni and micron-Ni in terms of stress/strain levels, reconfirming the stress-free states defined in the preceding paragraph. Therefore, the corresponding apparent strain is entirely due to the instrument resolution, i.e. , and there are no contributions of strain and grain size from the samples in this stage. Our graphic approach using Eq.2demonstrates that the instrument contribution to the Bragg peak broadening (in the unit of Δd and further in strain and stress) can be quantified by the sample itself as long as a stress-free state is obtained through high-temperature annealing of the polycrystalline materials. The true instrument contribution is usually difficult to characterize, particularly in energy-dispersive diffraction, due to the complexities of diffraction optics and instrument calibration. In addition, the presence of residual strains and crystal defects such as dislocations in the starting powders would further complicate the de-convolution of the diffraction profiles. The Fig. 9 is a graphic de-convolution of all kinds of contributions to the apparent stress and a complete high-temperature annealing to a stress-free state provides the base line for the thermo-mechanics characterization. The graphic derivation of thermo-mechanics using Eq.2is important not only for a comprehensive understanding of constitutive behaviors but also for the correct application of the peak-profile analysis method.
High-T Grain Growth and Annealing of Surface Strain of Nano-Crystals
Dislocation Densities in Nanocrystalline Ni
where b is the modulus of the Burges vector of the dislocations, A is a constant that can be taken as 3.3 , and C is a contrast factor which depends on the elastic anisotropy of the material and can be characterized by the ratios of C 44/(C 11 C 12) and C 12/C 44, where C 11 C 12, and C 44 are the elastic constants. All other parameters in Eq. 6 have the same meanings as in Eq. 2. More details on the data analysis using Eq. 6 were presented in Ref. .
Ashby  suggested that the dislocations in plastically deformed crystals can be separated into “geometrically necessary” dislocations (those associated with the existence of grain boundaries, in the present case) and “statistically stored” dislocations (glissile dislocations participating in the plastic deformation). It is important to note in Fig. 13 that there is a wide annealing temperature range where the total dislocation density decreases significantly (by a factor of ∼3) while the grain size remains approximately constant. The constancy of the grain size suggests that the density of “geometrically necessary” dislocations is not changing in this annealing temperature range and that the observed decrease in total dislocation density is due to the annihilation of the “statistically stored” dislocations that were generated by the heavy deformation of the ball milling process. At higher annealing temperatures, the grain size increases and this must correspond to a decrease in the density of geometrically necessary dislocations. Clearly, these two different types of dislocations in the Ni nanocrystals are correlated with the grain size variation. Also note that in the Ungar method the dislocation density is a parameter that characterizes the surface/residual strains caused by crystalline dislocations. Therefore, although it is not parametrically equivalent to the surface strain determined in Fig. 12, both of them describe the similar physical performances of the nanocrystals, as demonstrated by the similar trends of variation with annealing temperature in Figs. 12 and 13. As high-T annealing becomes more effective at T > 900 K, the surface strain approaches the instrument baseline of εins. = 0.005 (Fig. 12) and the dislocation density becomes nearly zero (Fig. 13). This difference is primarily due to the fact that the Δd in Eq. 6 or Ungar approach has already subtracted instrumental contribution to the peak broadening.
An Inverse Hall–Petch Effect in Nanocrystalline Ni99Fe1Alloy
where H 0 and k are material constants. This Hall–Petch relation has been explained by several models, such as the pile-up of dislocations ahead of grain boundaries [47, 48], grain boundary acting as a source of dislocations , and the influence of grain size on the dislocation density (under the assumption that dislocation density is inversely proportional to grain size) [54, 55].
The Hall–Petch relation is fairly well obeyed in crystalline alloys with grain sizes ranging from tens of nanometers to microns. It often fails, however, in alloys with grain sizes in the range 3–20 nm. Most nanocrystalline materials that do not obey the Hall Petch were first prepared in the smallest grain size possible (e.g. using techniques such as high-energy ball milling, electrodeposition, or gas condensation) and then were annealed (at increasingly higher temperatures) to increase their grain size. In materials prepared this way, the strength increased with increasing grain size and thus these materials were said to obey an inverse (or abnormal) Hall–Petch relationship [56, 58–66, 66]. The inverse Hall–Petch effect has been attributed to factors such as (i) a decrease in dislocation line tension with decreasing grain size ; (ii) the difficulty of generating dislocation pile-ups within grains having sizes less than a critical value ; (iii) a contribution to plasticity from grain-boundary diffusion creep [69, 71, 71], grain-boundary sliding [72, 73] or grain-boundary shear ; (iv) an overall softening with decreasing grain size due to the increase in the density of triple junctions [75, 76] or grain boundaries [77, 78]; (v) a reduced ability of the grain boundaries to obstruct the dislocation motion due to the decrease in the interfacial excess volume and energy ; (vi) atomic ordering near grain boundaries and triple junctions ; and (vii) the competition between dislocation emission (from within the grain boundaries) and grain-boundary sliding . Koch and Narayan  reviewed the literature prior to 2001 and suggested that in several instances the observed inverse Hall–Petch effect could be due to artifacts in the nanocrystalline materials such as porosity and/or amorphous inclusions. In spite of this extensive research, the observation of an inverse Hall–Petch relation upon increasing the grain size of nanocrystalline materials by annealing remains poorly understood. We studied the hardness-grain size relation in nanocrystalline Ni and find inverse Hall–Petch relation. We attribute our observed inverse Hall–Petch relation to impurity (Fe) segregating to grain boundaries.
The starting nanocrystalline Ni powders were prepared using the methods described in “Elastic Softening in Nanocrystalline Nickel Metals”. Following synthesis by ball milling, the powders were annealed in the same glove-box at increasing temperatures. After each 1-h anneal, the powders were rapidly cooled inside the glove box. The annealed powders were then fixed in epoxy resin. The hardened particles/epoxy-resin composites were mechanically polished using a 0.3 μm alumina paste and tested on a Micromet-4 to obtain their microhardness. Each reported microhardness value is the average of 10–20 measurements.
Since the inverse Hall–Petch relationship is observed in our nanocrystalline Ni (containing ∼1 at% Fe) but not in ultra-pure nanocrystalline Fe, studied using the same experimental methods , it is not unreasonable to assume that the inverse Hall–Petch relationship observed upon annealing nanocrystalline Ni is apparently due to the segregation of solutes to grain boundaries. Two previous studies on ball milled Fe seem to confirm our conclusions. Malow and Koch  ball-milled 99.9% pure Fe to achieve an initial grain size of ∼13 nm. This powder was sequentially annealed and the hardness was measured as a function of grain size. Here the Hardness versus L −1/2 followed a normal Hall–Petch relation. This contrasts with the experiments of Kahn et al.  who started with 98.5% pure Fe (the type of impurities were not specified) and added stearic acid [CH3(CH2)16CO2H] to the milling vial to minimize the agglomeration of the powder during ball milling. This additive most likely introduced additional impurities in the nanocrystalline product. The grain size of the as-prepared powder was 16 nm. Increasing the grain size to 23 nm (by annealing) caused the hardness to increase by 27%, in violation of the Hall–Petch relation . Then, a further increase in grain size (by annealing at higher temperatures) caused the hardness to decrease, in agreement with the Hall–Petch relation.
Several mechanisms may contribute concurrently to the plastic deformation of nanocrystalline materials (grain-boundary sliding, grain-boundary rotation, and the generation of dislocations at grain-boundaries) . All of these may be affected by the segregated solutes. Segregation of solutes and impurities in grain boundary may lead to three effects: (1) lowering the grain boundary energy, enabling the formation of low-energy grain boundary, (2) lowering the grain boundary free volume and thus the grain boundary diffusion coefficient, and (3) decreasing the stress gradient in the grain boundary regions. All of these three effects may increase the resistance for grain-boundary sliding, grain-boundary rotation, and the generation of dislocations at grain-boundaries. This reveals increased hardness of in annealed nanocrystalline materials.
Hardness increase induced by annealing has also been also frequently observed in plastically deformed large-grained polycrystalline materials. This phenomenon has been named as a “strain-ageing hardening” effect which means annealing (ageing) the deformed materials leads to hardening. In Fe97Si3 alloy (grain size = 30 μm) that was plastically deformed to ∼20% strain, annealing at 573 K for an hour increases the hardness by ∼4.6% . Origin of this increased hardness, however, is different than that in our nanocrystalline Ni. In plastically deformed large-grained polycrystalline materials, the major resistance for further plastic deformation comes from the long-range stress field of multiplicated dislocations. Annealing can segregate Si to the multiplicated dislocations, increasing the stress that is needed to move these dislocations.
We have conducted highP–T synchrotron X-ray and time-of-flight neutron diffraction experiments as well as indentation measurements to study equation of state, constitutive properties, and hardness on nanocrystalline and bulk nickel. Our results present a clear evidence of elastic softening in nanocrystalline Ni as compared with the bulk nickel. It is also observed that the bulk moduli determined using the “apparent lattice parameters” are 17–18% lower at the smaller diffraction vectors (Q = 2π/d) than those at the largerQ values. These findings support the results of molecular dynamics simulation and a generalized model of a nanocrystal with expanded surface layer. Based on the peak-profile analysis of diffraction data, the yield strength for nano-Ni is determined to be 2.35 GPa, more than three times higher than that of bulk Ni. Contrary to tensile experiments of uniaxial loading, we observe significant work-hardening for the nano-Ni in high-pressure plastic deformation stage, whereas the micron-Ni experiences minor high-pressure work-softening and considerable energy dissipation into heat. The significantly reduced energy dissipation for the nano-Ni during the loading-unloading cycle indicates that the nanostructured materials can endure much greater mechanical fatigue in cyclic loadings. Nano-Ni exhibits grain crushing in the elastic stage of deformation but steady grain growth during bulk plastic deformation under high-pressure loading. During the high-temperature annealing, Ni nanocrystals show drastic stress reduction with increasing temperature and grain growth above 573 K. The rate of grain growth at high temperature, however, is considerably smaller at 7.4 GPa than that at atmospheric pressure, indicating that pressure is an effective thermodynamic parameter for controlling the crystallization process. From micro-indentation measurements, our analysis suggests that the inverse Hall–Petch effect observed in the annealed nanocrystalline Ni of different grain size can be ascribed to the impurity effects. Annealing allows impurity Fe to migrate to the grain boundaries, increasing the stress needed to initiate grain-boundary mediated plastic deformation in nanocrystalline Ni.
Los Alamos National Laboratory is operated by Los Alamos National Security LLC under DOE contract DE-AC52-06NA25396. This work has benefited from the use of the Lujan Neutron Scattering Center at LANSCE, which is funded by the U.S. Department of Energy’s Office of Basic Energy Sciences. This work was also supported by the Laboratory Directed Research & Development (LDRD) program of the Los Alamos National Laboratory. The highP–T X-ray diffraction experiments were carried out at the beamlines X17B2 of National Synchrotron Light Source, Brookhaven National Laboratory, which is supported by the Consortium for Materials Properties Research in Earth Sciences (COMPRES) under NSF Cooperative Agreement EAR 01-35554.
- Chen CC, Herhold AB, Johnson CS, Alivisatos AP: Science. 1997, 276: 398. COI number [1:CAS:528:DyaK2sXis1Khurg%3D] 10.1126/science.276.5311.398View ArticleGoogle Scholar
- Goldstein AN, Echer CM, Alivisatos AP: Science. 1992, 256: 1425. COI number [1:CAS:528:DyaK38Xks1Sju74%3D] 10.1126/science.256.5062.1425View ArticleGoogle Scholar
- Chen J, Schmidt N, Chen JH, Zhang J, Wang L, Weidner DJ: J. Mat. Sci.. 2005, 40: 5763. COI number [1:CAS:528:DC%2BD2MXhtFaksL7E] 10.1007/s10853-005-2476-8View ArticleGoogle Scholar
- Zhao Y, Zhang J, Clausen B, Shen TD, Gray GT, Wang L: Nano Lett.. 2007, 7: 426. COI number [1:CAS:528:DC%2BD28XhtlehsrzO] 10.1021/nl062685sView ArticleGoogle Scholar
- Tolbert SH, Alivisatos AP: Annu. Rev. Phys. Chem.. 1995, 46: 595. COI number [1:CAS:528:DyaK2MXptlOisr4%3D] 10.1146/annurev.pc.46.100195.003115View ArticleGoogle Scholar
- Wang Z, Zhao Y, Schiferl D, Zha C, Downs R, Sekine T: Appl. Phys. Lett.. 2003, 83: 3174. COI number [1:CAS:528:DC%2BD3sXotVaqsro%3D] 10.1063/1.1618365View ArticleGoogle Scholar
- Wang Z, Zhao Y, Schiferl D, Zha C, Downs R: Appl. Phys. Lett.. 2004, 85: 124. COI number [1:CAS:528:DC%2BD2cXlsVagsLk%3D] 10.1063/1.1768298View ArticleGoogle Scholar
- Jiang JZ, Olsen JS, Gerward L, Morup S: Europhys. Lett.. 1998, 44: 620. COI number [1:CAS:528:DyaK1cXnvFyktLs%3D] 10.1209/epl/i1998-00563-6View ArticleGoogle Scholar
- Van Buuren T, Dinh LN, Chase LL, Siekhaus WJ, Terminello LJ: Phys. Rev. Lett.. 1998, 80: 3803. COI number [1:CAS:528:DyaK1cXisVGrurs%3D] 10.1103/PhysRevLett.80.3803View ArticleGoogle Scholar
- Chen B, Penwell D, Kruger MB: Solid State Comm.. 2000, 115: 191. COI number [1:CAS:528:DC%2BD3cXkt1artL8%3D] 10.1016/S0038-1098(00)00160-5View ArticleGoogle Scholar
- Rekhi S, Saxena SK, Ahuja R, Johansson B, Hu J: J. Mat. Sci.. 2001, 36: 4719. COI number [1:CAS:528:DC%2BD3MXosVyqs78%3D] 10.1023/A:1017974904559View ArticleGoogle Scholar
- Budrovic Z, Van Swygenhoven H, Derlet PM, Van Petegem S, Schmitt B: Science. 2004, 304: 273. COI number [1:CAS:528:DC%2BD2cXivV2isLo%3D] 10.1126/science.1095071View ArticleGoogle Scholar
- Shan ZW, Stach EA, Wiezorek JMK, Knapp JA, Follstaedt DM, Mao SX: Science. 2004, 305: 654. COI number [1:CAS:528:DC%2BD2cXmtFWru7Y%3D] 10.1126/science.1098741View ArticleGoogle Scholar
- Bonetti E, Campari EG, Pasquini L, et al.: J. Appl. Phys.. 1998, 84: 4219. COI number [1:CAS:528:DyaK1cXmtFKgt70%3D] 10.1063/1.368639View ArticleGoogle Scholar
- Valiev RZ, Korznikova GF, Mulyukov KY, et al.: Philos. Mag. B. 1997, 75: 803. COI number [1:CAS:528:DyaK2sXjvFKhs7o%3D]View ArticleGoogle Scholar
- Zhang J, Zhao Y, Palosz B: Appl. Phys. Lett.. 2007, 90: 043112. COI number [1:CAS:528:DC%2BD2sXhsFyltr8%3D] 10.1063/1.2435325View ArticleGoogle Scholar
- Shen TD, Schwarz RB, Feng S, Swadener JG, Huang JY, Tang M, Zhang Jianzhong, Vogel SC, Zhao Yusheng: Acta Mater.. 2007, 55: 5007. COI number [1:CAS:528:DC%2BD2sXovFWisLk%3D] 10.1016/j.actamat.2007.05.018View ArticleGoogle Scholar
- Y. Zhao, J. Zhang, submitted to Int. J. Plast. (2007)Google Scholar
- Gleiter H: Prog. Mat. Sci.. 1989, 33: 223. COI number [1:CAS:528:DyaK3MXhslWnt7w%3D] 10.1016/0079-6425(89)90001-7View ArticleGoogle Scholar
- Shen TD, Koch CC, Tsui TY, Pharr GM: J. Mater. Res.. 1995, 10: 2892. COI number [1:CAS:528:DyaK2MXptVChtLg%3D] 10.1557/JMR.1995.2892View ArticleGoogle Scholar
- Lupo JA, Sabochick MJ: Nanostruct. Mater.. 1992, 1: 131. COI number [1:CAS:528:DyaK38XkvFejsbw%3D] 10.1016/0965-9773(92)90065-6View ArticleGoogle Scholar
- Latapie A, Farkas D: Scripta Mater.. 2003, 48: 611. COI number [1:CAS:528:DC%2BD3sXisF2mtQ%3D%3D] 10.1016/S1359-6462(02)00467-0View ArticleGoogle Scholar
- Chen B, Penwell D, Kruger MB, Yue AF, Fultz BJ: Appl. Phys.. 2001, 89: 4794. COI number [1:CAS:528:DC%2BD3MXivFWisr4%3D] 10.1063/1.1357780View ArticleGoogle Scholar
- Wang ZW, Pischedda V, Saxena SK, Lazor P: Solid State Commun.. 2002, 121: 275. COI number [1:CAS:528:DC%2BD38XhtVSlsL4%3D] 10.1016/S0038-1098(01)00509-9View ArticleGoogle Scholar
- Hazen RM: Science. 1993, 159: 206. 10.1126/science.259.5092.206View ArticleGoogle Scholar
- Zhang J, Kostak P: Phys. Earth Planet. Int.. 2002, 129: 301. COI number [1:CAS:528:DC%2BD38Xhs1ynu7Y%3D] 10.1016/S0031-9201(01)00296-5View ArticleGoogle Scholar
- Weidner DJ, Vaughan MT, Ko J, Wang Y, Liu X, Yeganeh-haeri A, Pacalo RE, Zhao Y: High-Pressure Research: Application to Earth and Planetary Sciences. Edited by: Syono Y., Manghnani M.H.. AGU, Washington DC; 1992:13–17.View ArticleGoogle Scholar
- Decker DL: J. Appl. Phys.. 1971, 42: 3239. COI number [1:CAS:528:DyaE3MXks1Olur8%3D] 10.1063/1.1660714View ArticleGoogle Scholar
- McKeehan LW: Phys. Rev.. 1923, 21: 402. COI number [1:CAS:528:DyaB3sXhtlCntA%3D%3D] 10.1103/PhysRev.21.402View ArticleGoogle Scholar
- Birch F: J. Geophys. Res.. 1978, 83: 1257. COI number [1:CAS:528:DyaE1cXhslOgur4%3D] 10.1029/JB083iB03p01257View ArticleGoogle Scholar
- Trapp S, Limbach CT, Gonser U, Campbell SJ, Gleiter H: Phys. Rev. Lett.. 1995, 75: 3761. 10.1103/PhysRevLett.75.3760View ArticleGoogle Scholar
- Palosz B, Stel’makh S, Grzanka E, Gierlotka S, Pielaszek R, Bismayer U, Werner S, Palosz W: J. Phys. Condens. Matter.. 2003, 15: 1. 10.1088/0953-8984/15/2/301View ArticleGoogle Scholar
- Palosz B, Stel’makh S, Grzanka E, Gierlotka S, Zhao Y, Palosz W: Mat. Res. Soc. Symp. Proc.. 2003, 778: 29. COI number [1:CAS:528:DC%2BD3sXos1Gntb8%3D]Google Scholar
- Palosz B, Grzanka E, Gierlotka S, Stel’makh S, Pielaszek R, Bismayer U, Neuefeind J, Weber HP, Proffen T, Von Dreele R, Palosz W: Z. Kristallogr.. 2002, 217: 497. COI number [1:CAS:528:DC%2BD3sXht1aisQ%3D%3D] 10.1524/zkri.217.10.497.20795View ArticleGoogle Scholar
- Zhao SJ, Albe K, Hahn H: Scripta Mater.. 2006, 55: 473. COI number [1:CAS:528:DC%2BD28Xmt1amsLg%3D] 10.1016/j.scriptamat.2006.04.043View ArticleGoogle Scholar
- Weidner DJ, Wang Y, Vaughan MT: Science. 1994, 266: 419. COI number [1:CAS:528:DyaK2cXntFanu7w%3D] 10.1126/science.266.5184.419View ArticleGoogle Scholar
- Zhang J, Wang L, Weidner DJ, Ucchida T, Xu J: Am. Mineral.. 2002, 87: 1005. COI number [1:CAS:528:DC%2BD38Xlt1aks7w%3D]Google Scholar
- Brown DW, Bourke MAM, Clausen B, Holden TM, Tome CN, Varma RA: Metall. Mater. Trans. A. 2003, 34A: 1439. COI number [1:CAS:528:DC%2BD3sXlsV2rs78%3D] 10.1007/s11661-003-0256-0View ArticleGoogle Scholar
- Qian J, Pantea C, Zhang J, Zhao Y, Wang Y, Uchida T: J. Am. Ceramic Soc.. 2005, 88: 903. COI number [1:CAS:528:DC%2BD2MXjsFegtbs%3D] 10.1111/j.1551-2916.2005.00163.xView ArticleGoogle Scholar
- Williamson GK, Hall WH: Acta Metall.. 1953, 1: 22. COI number [1:CAS:528:DyaG3sXitFCquw%3D%3D] 10.1016/0001-6160(53)90006-6View ArticleGoogle Scholar
- Gerward L, Morup S, Topsoe H: J. Appl. Phys.. 1976, 47: 822. 10.1063/1.322714View ArticleGoogle Scholar
- Weidner DJ, Wang Y, Vaughan MT: Geophys. Res. Lett.. 1994, 21: 753. 10.1029/93GL03549View ArticleGoogle Scholar
- Revesz A, Ungar T, Borbely A, Lendvai J: Nanostruct. Mater.. 1996, 7: 779. COI number [1:CAS:528:DyaK28XmsVSktLo%3D] 10.1016/S0965-9773(96)00048-7View ArticleGoogle Scholar
- Ungar T, Tichy G: Phys Status Solidi A. 1999, 171: 425. COI number [1:CAS:528:DyaK1MXhs1OqtLw%3D] 10.1002/(SICI)1521-396X(199902)171:2<425::AID-PSSA425>3.0.CO;2-WView ArticleGoogle Scholar
- Ungar T, Dragomir I, Revesz A, Borbely A: J Appl Crystallogr. 1999, 32: 992. COI number [1:CAS:528:DyaK1MXmslaltbY%3D] 10.1107/S0021889899009334View ArticleGoogle Scholar
- Wenk HR, Lutterotti L, Vogel S: Nucl. Instrum. Methods A. 2003, 515: 575. COI number [1:CAS:528:DC%2BD3sXpt1Gnsrg%3D] 10.1016/j.nima.2003.05.001View ArticleGoogle Scholar
- Hall EO: Proc. Phys. Soc.. 1951, B64: 747. COI number [1:CAS:528:DyaG38Xms1GktQ%3D%3D]View ArticleGoogle Scholar
- Petch NJ: J. Iron Steel Inst.. 1953, 174: 25. COI number [1:CAS:528:DyaG3sXktFSjtQ%3D%3D]Google Scholar
- A.C. Larson, R.B. Von Dreele, Los Alamos National Laboratory Report LAUR 86–748 (2004)Google Scholar
- Zhao Y, He D, Daemen LL, Huang J, Shen TD, Schwarz RB, Zhu Y, Bish DL, Zhang J, Shen G, Liu Z, Qian J, Zerda TW: J. Mat. Res.. 2002, 17: 3139. COI number [1:CAS:528:DC%2BD38XpsVOgt78%3D] 10.1557/JMR.2002.0454View ArticleGoogle Scholar
- Zhao Y, Qian J, Daemen LL, Pantea C, Zhang J, Voronin G, Zerda TW: Appl. Phys. Lett.. 2004, 84: 1356. COI number [1:CAS:528:DC%2BD2cXhsVylu70%3D] 10.1063/1.1650556View ArticleGoogle Scholar
- Ashby MF: Philos. Mag.. 1970, 21: 399. COI number [1:CAS:528:DyaE3cXmtVShug%3D%3D] 10.1080/14786437008238426View ArticleGoogle Scholar
- Li JCM: Trans. AIME. 1963, 227: 239. COI number [1:CAS:528:DyaF3sXksFenug%3D%3D]Google Scholar
- Conrad H: Electron Microscopy and Strength of Crystals. Edited by: Thomas G., Washburn J.. Interscience, New York; 1963:299.Google Scholar
- Thompson AW, Baskes MI, Flanagan WF: Acta Metall.. 1973, 21: 1017. COI number [1:CAS:528:DyaE3sXlt1ymsbw%3D] 10.1016/0001-6160(73)90158-2View ArticleGoogle Scholar
- Chokshi AH, Rosen A, Karch J, Gleiter H: Scripta Metall.. 1989, 23: 1679. COI number [1:CAS:528:DyaL1MXmtFyju7g%3D] 10.1016/0036-9748(89)90342-6View ArticleGoogle Scholar
- Lu K, Wei WD, Wang JT: Scripta Metall. Mater.. 1990, 24: 2319. COI number [1:CAS:528:DyaK3MXivVelsA%3D%3D] 10.1016/0956-716X(90)90086-VView ArticleGoogle Scholar
- Christman T, Jain M: Scripta Metall. Mater.. 1991, 25: 767. COI number [1:CAS:528:DyaK3MXitFWrt7s%3D] 10.1016/0956-716X(91)90222-MView ArticleGoogle Scholar
- Kim DK, Okazaki K: Mater. Sci. Forum. 1992, 88–90: 553. 10.4028/www.scientific.net/MSF.88-90.553View ArticleGoogle Scholar
- Chang H, Altstetter CJ, Averback RS: J. Mater. Res.. 1992, 7: 2962. COI number [1:CAS:528:DyaK3sXhtVSrtg%3D%3D] 10.1557/JMR.1992.2962View ArticleGoogle Scholar
- Liu XD, Wang JT, Hu ZQ, Ding BZ: Mater. Sci. Eng.. 1993, A169: L17. COI number [1:CAS:528:DyaK3sXmsFCntbg%3D]View ArticleGoogle Scholar
- Alves H, Ferreira M, Köster U, Müller B: Mater. Sci. Forum. 1996, 225–227: 769.View ArticleGoogle Scholar
- Volpp T, Göring E, Kuschke WM, Artz E: Nanostruct. Mater.. 1997, 8: 855. COI number [1:CAS:528:DyaK1cXhs1ejsL0%3D] 10.1016/S0965-9773(98)00019-1View ArticleGoogle Scholar
- Kahn AS, Zhang H, Takacs L: Int. J. Plastic.. 2000, 16: 1459. 10.1016/S0749-6419(00)00023-1View ArticleGoogle Scholar
- Guicciardi S, Sciti D, Melandri C, Bellosi A: J. Am. Ceram. Soc.. 2004, 87: 2101. COI number [1:CAS:528:DC%2BD2cXhtFagurjF] 10.1111/j.1151-2916.2004.tb06366.xView ArticleGoogle Scholar
- Bellosi A, Vicens J, Medri V, Guicciardi S: Appl. Phys. A. 2005, 81: 1045. COI number [1:CAS:528:DC%2BD2MXmvFWjtrs%3D] 10.1007/s00339-004-2935-0View ArticleGoogle Scholar
- Scattergood RO, Koch CC: Scripta Metall. Mater.. 1992, 27: 1195. COI number [1:CAS:528:DyaK38XmtFOrurY%3D] 10.1016/0956-716X(92)90598-9View ArticleGoogle Scholar
- Nieh TG, Wadsworth J: Scripta Metall. Mater.. 1991, 25: 955. COI number [1:CAS:528:DyaK3MXhvFShs7k%3D] 10.1016/0956-716X(91)90256-ZView ArticleGoogle Scholar
- Masumura RA, Hazzledine PM, Pande CS: Acta Mater.. 1998, 46: 4527. COI number [1:CAS:528:DyaK1cXls12murk%3D] 10.1016/S1359-6454(98)00150-5View ArticleGoogle Scholar
- Yamakov V, Wolf D, Phillpot SH, Gleiter H: Acta Mater.. 2002, 50: 61. COI number [1:CAS:528:DC%2BD3MXptFensLY%3D] 10.1016/S1359-6454(01)00329-9View ArticleGoogle Scholar
- Kim HS, Estrin Y: Acta Mater.. 2006, 53: 765. COI number [1:CAS:528:DC%2BD2cXhtVyks7fF] 10.1016/j.actamat.2004.10.028View ArticleGoogle Scholar
- Hahn H, Mondal P, Padmanabhan KA: Nanostruct. Mater.. 1997, 9: 603. COI number [1:CAS:528:DyaK2sXnt1WjsbY%3D] 10.1016/S0965-9773(97)00135-9View ArticleGoogle Scholar
- Schiotz J, Vegge T, Di Tolla FD, Jacobsen KW: Phys. Rev. B. 1999, 60: 11971. COI number [1:CAS:528:DyaK1MXmvFOgsb0%3D] 10.1103/PhysRevB.60.11971View ArticleGoogle Scholar
- Conrad H, Narayan J: Scripta Mater.. 2000, 42: 1025. COI number [1:CAS:528:DC%2BD3cXjslGqtrs%3D] 10.1016/S1359-6462(00)00320-1View ArticleGoogle Scholar
- Palumbo G, Erb U, Aust KT: Scripta Metall. Mater.. 1990, 24: 2347. COI number [1:CAS:528:DyaK3MXivVelsQ%3D%3D] 10.1016/0956-716X(90)90091-TView ArticleGoogle Scholar
- Xiang Q, Guo XM: Int. J. Solids Struct.. 2006, 43: 7793. COI number [1:CAS:528:DC%2BD28XhtlCisLvM] 10.1016/j.ijsolstr.2006.04.015View ArticleGoogle Scholar
- Carsley JE, Ning J, Milligan WW, Hackney SA, Aifantis EC: Nanostruct. Mater.. 1995, 5: 441. COI number [1:CAS:528:DyaK2MXmtFOmt7w%3D] 10.1016/0965-9773(95)00257-FView ArticleGoogle Scholar
- Fan GJ, Choo H, Liaw PK, Lavernia EJ: Mater. Sci. Eng.. 2005, A409: 243. COI number [1:CAS:528:DC%2BD2MXht1aqtbrM]View ArticleGoogle Scholar
- Lu K, Sui ML: Scripta Metall. Mater.. 1993, 28: 1465. COI number [1:CAS:528:DyaK3sXktlaktL0%3D] 10.1016/0956-716X(93)90576-EView ArticleGoogle Scholar
- Hasnaoui A, Van Swygenhoven H, Derlet PM: Acta Mater.. 2002, 50: 3927. COI number [1:CAS:528:DC%2BD38Xms1amt7k%3D] 10.1016/S1359-6454(02)00195-7View ArticleGoogle Scholar
- Farkas D, Curtin WA: Mater. Sci. Eng.. 2005, A412: 316. COI number [1:CAS:528:DC%2BD2MXht1GnsLfF]View ArticleGoogle Scholar
- Koch CC, Narayan J: Mat. Res. Soc. Symp. Proc.. 2001, 634: B511.Google Scholar
- Malow TR, Koch CC: Metall. Mater. Trans.. 1998, A29: 2285. 10.1007/s11661-998-0106-1View ArticleGoogle Scholar
- Meyers MA, Mishra A, Benson DJ: Prog. Mater. Sci.. 2006, 51: 427. COI number [1:CAS:528:DC%2BD28XhtlCrs7s%3D] 10.1016/j.pmatsci.2005.08.003View ArticleGoogle Scholar