Generalized type III internal stress from interfaces,triple junctions and other microstructural components in nanocrystalline materials

The microstructure in polycrystalline materials consists of four types of geometric objects: grain cells, grain boundaries, triple junctions and vertex points. Each of them contributes to internal stress differently. Due to experimental limitations, the internal stresses associated with the microstructural components are difficult to acquire directly, particularly for polycrystalline materials with nanometer-scale grain sizes. Using newly developed computational methods, we obtained the type III internal stress associated with each of these microstructural objects in a stress-free nanocrystalline Cu. We found significant variation of the internal stresses from grain to grain, and their magnitudes descended in the order of vertex point, triple junction, grain boundary and grain cell. We also examined the effect of grain size and temperature. The change in the internal stresses inside the grains is found to follow a scaling relation of Ad^?x, using the mean grain diameter d from our results. For pressure, we found x = 1 and the effective interface stress A ～ 1 N m^?1, and for shear stress x = 0.75 and A ～ 14.12 N m^?1. On the other hand, the directly calculated interface stress is about 0.32–0.35 GPa for hydrostatic pressure and 12.45–12.60 GPa for von Mises shear stress. We discuss issues in treating the two-dimensional interface stress and one-dimensional triple junction line tension in nanocrystalline materials, as well as the potential impact of the type III internal stress on mechanical behavior of poly- and nano-crytalline materials.     

Properties of nanocrystalline and nanocomposite WxZr1−x thin films deposited by co-sputtering

W_xZr_1?x thin films were deposited at room temperature on glass substrates by co-sputtering tungsten and zirconium targets in argon. The composition was found in the range 0 ≤ x ≤ 0.81. The grain size deduced from X-ray diffraction analysis ranged from 1.3 nm to 16 nm depending on the composition. The events in the resistivity, optical reflectivity and thickness evolutions were correlated with the X-ray diffraction analysis. Depending on the composition, the local organization can be attributed to a nanocrystalline solid solution of W in Zr, to a nanocomposite structure involving ZrW₂ nanograins embedded in an amorphous matrix, to ZrW₂ Laves phase nanograins and to a nanocrystalline solid solution of Zr in W. For 0 < x ≤ 0.72, the equivalent grain size is very small (less than 2 nm) and the evolution of the resistivity can be fitted by the estimated volume of the material perturbed by the grain boundaries.     

Microstructural evolution in copper subjected to severe plastic deformation: Experiments and analysis

The evolution of microstructure and the mechanical response of copper subjected to severe plastic deformation using equal channel angular pressing (ECAP) was investigated. Samples were subjected to ECAP under three different processing routes: B_C, A and C. The microstructural refinement was dependent on processing with route B_C being the most effective. The mechanical response is modeled by an equation containing two dislocation evolution terms: one for the cells/subgrain interiors and one for the cells/subgrain walls. The deformation structure evolves from elongated dislocation cells to subgrains to equiaxed grains with diameters of ∼200–500 nm. The misorientation between adjacent regions, measured by electron backscatter diffraction, gradually increases. The mechanical response is well represented by a Voce equation with a saturation stress of 450 MPa. Interestingly, the microstructures produced through adiabatic shear localization during high strain rate deformation and ECAP are very similar, leading to the same grain size. It is shown that both processes have very close Zener–Hollomon parameters (ln Z ∼ 25). Calculations show that grain boundaries with size of 200 nm can rotate by ∼30° during ECAP, thereby generating and retaining a steady-state equiaxed structure. This is confirmed by a grain-boundary mobility calculation which shows that their velocity is 40 nm/s for a 200 nm grain size at 350 K, which is typical of an ECAP process. This can lead to the grain-boundary movement necessary to retain an equiaxed structure.     

Crystallization of amorphous ceria solid solutions

Next-generation micro-solid oxide fuel cells for portable devices require nanocrystalline thin film electrolytes in order to allow fuel cell fabrication on chips at low operating temperatures and with high fuel cell power outputs. In this study amorphous gadolinia-doped ceria (Ce_0.8Gd_0.2O_1.9−x) thin film electrolytes were fabricated by spray pyrolysis and their crystallization to nanocrystalline microstructures was investigated by means of X-ray diffraction and transmission electron microscopy. At temperatures higher than 500 °C the amorphous films crystallize to a biphasic ceramic that is amorphous and nanocrystalline. The driving force for the crystallization is the reduction of the free enthalpy resulting from the transformation of amorphous into crystalline material. Self-limited grain growth kinetics prevail for the nanocrystalline grains where stable microstructures are established after short dwell times. A transition to classical curvature-driven grain growth kinetics occurs when the fully crystalline state is reached for average grain sizes larger than 140 nm and annealing temperatures higher than 1100 °C.     

A corrosion study of nanocrystalline copper thin films

Thin nanocrystalline, compact films, based on the copper–nitrogen system, up to 2.5 μm thickness and 3.5% nitrogen, were deposited by magnetron sputtering at different partial pressure ratios of N₂ and Ar, without formation of Cu_xN compounds, the nitrogen concentration influencing grain size (down to 30 nm) and film homogeneity. Electrochemical corrosion properties were investigated using polarization curves and electrochemical impedance spectroscopy in 0.5 M NaCl aqueous solution, and compared with pure bulk copper; morphology was examined by scanning electron microscopy. Significant variations in corrosion currents between samples were attributed to grain size and structural defects on the grain boundaries.     

What is the theoretical density of a nanocrystalline material?

We prepared nanocrystalline Ni by a severe deformation method – high-energy ball milling – and collected neutron diffraction patterns during the annealing of nanocrystalline Ni. Analyzing the neutron diffraction patterns provides the lattice parameter, dislocation density and grain size of nanocrystalline Ni. We found that a low-temperature (T < 260 °C) anneal annihilates the statistically stored dislocations whereas a high-temperature (T > 260 °C) anneal grows the nanograins. For T < 260 °C, where nanocrystalline Ni has a constant grain size, the excess volume is proportional to the density of statistically stored dislocations. For T > 260 °C, where the statistically stored dislocations are completely annealed out, the excess volume is inversely proportional to the grain size. However, 80% of the excess volume in our severely deformed nanocrystalline Ni is due to the statistically stored dislocations. We finally used our experimental data to derive the grain size dependence of the theoretical density of a nanocrystalline material free from excess dislocations. The derived theoretical density agrees well with the experimentally measured density of nanocrystalline metallic materials that are relatively free from deformation-induced defects.     

Correlation between the microstructure studied by X-ray line profile analysis and the strength of high-pressure-torsion processed Nb and Ta

Niobium and tantalum are two body centered cubic metals with very different elastic anisotropy. The A_z = 2 × c₄₄/(c₁₁?c₁₂) constant for Nb and Ta is 0.51 and 1.58, respectively. The submicron grain-size state of the two refractory metals was produced by the method of high-pressure torsion with different pressure values of 2 and 4 GPa for Nb, and 4 and 8 GPa for Ta, and two different deformations of 0.25 and 1.5 rotations, respectively, with equivalent strains of up to ～40. The dislocation density and the grain size were determined by high-resolution diffraction peak-profile analysis. The beam size on the specimen surface was 0.2 × 1 mm, allowing the sub-structure along the radius of the specimen to be characterized. The strength of the two metals was correlated with the dislocation density and the grain size. It is found that, though the grain size is well below 100 nm, the role of dislocations in the flow stress of these two metals is significantly greater than that of the grain size.     

Direct synthesis of varistor-grade doped nanocrystalline ZnO and its densification through a step-sintering technique

A direct synthesis of varistor-grade doped ZnO powder was attempted by simple hydrolysis followed by low-temperature refluxing (80 °C) in aqueous and alcoholic media. Rod like, one-dimensional nanocrystalline doped ZnO powders with crystallite size 24 nm and Brunauer–Emmett–Teller (BET) bulk surface area 22 m² g⁻¹ were synthesized. Sintering characteristics of these powders were analyzed under step-sintering coupled with rapid heating up to 1050 °C. The microstructural features and I–V characteristics of the step-sintered doped ZnO were compared with composite varistors. The study shows the advantage of the addition of nanosize doped varistor-grade ZnO as well as step-sintering for controlling grain size and improving varistor performance.     

Microstructural changes of nanocrystalline nickel during cold rolling

The microstructural changes of electrodeposited nanocrystalline Ni with an initial grain size of about ∼30–40 nm during cold rolling up to 76% thickness reduction have been studied using X-ray diffraction and transmission electron microscopy. In response to the cold deformation processing we observed significant changes in the scale and morphology of grains, defect content, as well as of crystallographic texture. Our experimental findings for nanocrystalline Ni are directly compared to the behavior of coarse-grained Ni. The role of the grain scale reduction to the nanometer regime is discussed with respect to the microstructural changes.     

Thermomechanical cyclic response of an ultrafine-grained NiTi shape memory alloy

We focus on the effects of ultrafine grains on the thermomechanical cyclic stability of martensitic phase transformation in Ni_49.7Ti_50.3 shape memory alloy fabricated using equal-channel angular extrusion (ECAE). The samples were ECAE-processed between 400 and 450 °C resulting in average grain sizes of 100–300 nm. Tensile failure experiments demonstrated that the strength differential between the onset of transformation and the macroscopic plastic yielding increases after ECAE. Such increase led to a notable improvement in the thermal cyclic stability under relatively high stresses. The experimental observations are attributed to the increase in critical stress level for dislocation slip due to grain refinement, change in transformation twinning mode in submicron grains, the presence of R-phase, and multi-martensite variants or a small fraction of untransforming grains due to grain boundary constraints. The effects of these microstructural factors on the transformation behavior are discussed in the light of transformation thermodynamics.     

Effects of stress ratio on fatigue crack propagation properties of submicron-thick free-standing copper films

The dominant mechanics and mechanisms of fatigue crack propagation in ca. 500 nm thick free-standing copper films were evaluated at the submicron level using fatigue crack propagation experiments at three stress ratios, R = 0.1, 0.5 and 0.8. Fatigue cracking initiated at the notch root and propagated stably under cyclic loading. The fatigue crack propagation rate (da/dN) vs. stress intensity factor range (ΔK) relation was dependent on the stress ratio R;da/dN, increases with increasing R. Plots of da/dN vs. the maximum stress intensity factor (K_max) exhibited coincident features in the high-K_max region (K_max ? 4.5 MPa m^1/2) irrespective of R, indicating that K_max is the dominant factor in fatigue crack propagation. In this region, the fatigue crack propagated in tensile fracture mode irrespective of the R value. The region ahead of the fatigue crack tip is plastically stretched by tensile deformation, causing necking deformation in the thickness direction and consequent chisel-point fracture. In contrast, in the low-K_max region (K_max < 4.5 MPa m^1/2), the da/dN vs. K_max function assumes higher values with decreasing R; in this region, the fracture mechanism depends on R. At the higher R value (R = 0.8), the fatigue crack propagates in the tensile fracture mode similar to that in the high-K_max region. On the other hand, at the lower R values (R = 0.1 and 0.5), a characteristic mechanism of fatigue crack propagation appears: within several grains, intrusions/extrusions form ahead of the crack tip along the Σ3 twin boundaries, and the fatigue crack propagates preferentially through the intrusions/extrusions.     

Texture,microstructure and mechanical properties of equiaxed ultrafine-grained Zr fabricated by accumulative roll bonding

The texture, microstructure and mechanical behavior of bulk ultrafine-grained (ufg) Zr fabricated by accumulative roll bonding (ARB) is investigated by electron backscatter diffraction, transmission electron microscopy and mechanical testing. A reasonably homogeneous and equiaxed ufg structure, with a large fraction of high angle boundaries (HABs, ∼70%), can be obtained in Zr after only two ARB cycles. The average grain size, counting only HABs (θ > 15°), is 400 nm. (Sub)grain size is equal to 320 nm. The yield stress and UTS values are nearly double those from conventionally processed Zr with only a slight loss of ductility. Optimum processing conditions include large thickness reductions per pass (ε ∼ 75%), which enhance grain refinement, and a rolling temperature (T ∼ 0.3T_m) at which a sufficient number of slip modes are activated, with an absence of significant grain growth. Grain refinement takes place by geometrical thinning and grain subdivision by the formation of geometrically necessary boundaries. The formation of equiaxed grains by geometric dynamic recrystallization is facilitated by enhanced diffusion due to adiabatic heating.     

Study of the effect of α irradiation on the microstructure and mechanical properties of nanocrystalline Ni

The effect of irradiation damage on the microstructure evolution and mechanical properties in nanocrystalline (nc) Ni with an average grain size of ～60 nm was studied. Samples were irradiated at doses of 1.6 × 10¹⁵, 2.3 × 10¹⁵, 5 × 10¹⁵ and 2.3 × 10¹⁶ He²⁺ cm^?2 by 12 MeV He ions at room temperature. Microstructural parameters like domain size and microstrain were studied in detail using the X-ray diffraction (XRD) technique with the simplified breadth method and Williamson–Hall analysis. The average domain size was found to decrease systematically with the increase in irradiation dose. Microscopic observations made with transmission electron microscopy showed dislocation loops and dislocation networks within the grain interior of the irradiated sample. In addition, irradiation at a higher dose showed small amounts of the sand-like black dots inside some grains, which could be due to the accumulation of point defects. Tensile tests performed on the irradiated sample were compared with unirradiated samples. The irradiated sample showed higher ultimate tensile strength and average work-hardening rate as compared to the unirradiated sample. Nanoindentation studies were performed to study the effect of irradiation on deformation parameters like strain rate sensitivity (m) and activation volume (V^*). The value of m was found to increase whereas V^* was found to decrease with increase in irradiation dose. Fracture surfaces of the tensile sample were investigated by SEM. The fracture morphology of the unirradiated sample showed dimpled rupture with much large dimple diameter and depth. The irradiated sample also showed dimple rupture but with much finer dimple diameter with wide size distribution and shallow depths.     

Preparation of WC nanoparticles by twice ball milling

In order to improve the ball milling efficiency of WC powders and thus to fabricate nano-grained WC–Co cemented carbides with high mechanical properties, WC nanoparticles were prepared by twice ball milling in nylon vessels. The best technology to disperse WC powders in alcohol was investigated at first. Based on the dispersion results, 2 wt.% PEG was used with La₂O₃ as additive to improve ball milling efficiency. The particle size, crystal structure, surface morphology and surface properties were tested by a laser particle sizer, XRD, FE-SEM and FT-IR, respectively. During the first ball milling, sample d achieved the best milling performance, including average particle size (168 nm) and grain size (27.2 nm) among samples a (pure WC), b (with PEG), c (with La₂O₃) and d (with PEG and La₂O₃). La₂O₃ could greatly decrease particle size and grain size while PEG could narrow particle size distribution. During the second milling, the particle size and grain size of sample d reached 89 nm and 13.2 nm at 96 h, respectively. The results indicated that twice ball milling can greatly improve particle size and grain size compared with the first ball milling, and further narrow the size distribution. In conclusion, multiple ball milling can reduce the particle size of certain powders with suitable milling technology.     

Void initiation in fcc metals: Effect of loading orientation and nanocrystalline effects

It is shown, through molecular dynamics simulations, that the emission and outward expansion of special dislocation loops, nucleated at the surface of nanosized voids, are responsible for the outward flux of matter, promoting their growth. Calculations performed for different orientations of the tensile axis, [0 0 1], [1 1 0] and [1 1 1], reveal new features of these loops for a face-centered cubic metal, copper, and show that their extremities remain attached to the surface of voids. There is a significant effect of the loading orientation on the sequence in which the loops form and interact. As a consequence, the initially spherical voids develop facets. Calculations reveal that loop emission occurs for voids with radii as low as 0.15 nm, containing two vacancies. This occurs at a von Mises stress approximately equal to 0.12G (where G is the shear modulus of the material), and is close to the stress at which dislocation loops nucleate homogeneously. The velocities of the leading partial dislocations are measured and found to be subsonic (～1000 m s^?1). It is shown, for nanocrystalline metals that void initiation takes place at grain boundaries and that their growth proceeds by grain boundary debonding and partial dislocation emission into the grains. The principal difference with monocrystals is that the voids do not become spherical and that their growth proceeds along the boundaries. Differences in stress states (hydrostatic and uniaxial strain) are discussed. The critical stress for void nucleation and growth in the nanocrystalline metal is considerably lower than in the monocrystalline case by virtue of the availability of nucleation sites at grain boundaries (von Mises stress ～0.05G). This suggests a hierarchy of nucleation sites in materials, starting with dispersed phases, triple points and grain boundaries, and proceeding with vacancy complexes up to divacancies.     

Microstructure characterization of nanocrystalline (Ti0.9W0.1) C prepared by mechanical alloying

The microstructural characteristics of nanocrystalline (Ti_0.9W_0.1)C during mechanical alloying were investigated by using X-ray diffraction. The diffraction crystallite size (DCS) and the microstrain of (Ti_0.9W_0.1) C ball milled powders have been determined according to various models. The Scherrer and the Stokes–Wilson relations, the Williamson–Hall plot and the Rietveld refinement methods have been employed. The Rietveld method seems to be the best since it gives homogeneous results. The results obtained showed that the (Ti_0.9W_0.1)C diffraction crystallite size decreases tremendously and its microstrain increases as the milling duration increases. With the further milling of the nanocrystalline (Ti_0.9W_0.1)C within the stage of the steady-state diffraction crystallite size (8–6 nm), we observed a grain boundary relaxation process that was manifested by evident decreases in the root-mean-square strain, as well as important increases in the dislocation density and the volume fraction. Thus, when the (DCS) is higher than the critical value (8 nm), the plastic deformation is governed by the dislocation sliding mechanism. In the contrary, when the (DCS) is lesser than 8 nm, the plastic deformation is governed by the grain-boundary sliding mechanism.     

Size effects on yield strength and strain hardening for ultra-thin Cu films with and without passivation: A study by synchrotron and bulge test techniques

We present a systematic study of the mechanical properties of different Cu, Ta/Cu and Ta/Cu/Ta films systems. By using a novel synchrotron-based tensile testing technique isothermal stress–strain curves for films as thin as 20 nm were obtained for the first time. In addition, freestanding Cu films with a minimum thickness of 80 nm were tested by a bulge testing technique. The effects of different surface and interface conditions, film thickness and grain size were investigated over a range of film thickness up to 1 μm. It is found that the plastic response scales strongly with film thickness but the effect of the interfacial structure is smaller than expected. By considering the complete grain size distribution and a change in deformation mechanism from full to partial dislocations in the smallest grains, the scaling behavior of all film systems can be described correctly by a modified dislocation source model. The nucleation of dissociated dislocations at the grain boundaries also explains the strongly reduced strain hardening for these films.     

Nanocrystalline Fe–C alloys produced by ball milling of iron and graphite

A series of nanocrystalline Fe–C alloys with different carbon concentrations (x_tot) up to 19.4 at.% (4.90 wt.%) are prepared by ball milling. The microstructures of these alloys are characterized by transmission electron microscopy and X-ray diffraction, and partitioning of carbon between grain boundaries and grain interiors is determined by atom probe tomography. It is found that the segregation of carbon to grain boundaries of α-ferrite can significantly reduce its grain size to a few nanometers. When the grain boundaries of ferrite are saturated with carbon, a metastable thermodynamic equilibrium between the matrix and the grain boundaries is approached, inducing a decreasing grain size with increasing x_tot. Eventually the size reaches a lower limit of about 6 nm in alloys with x_tot > 6.19 at.% (1.40 wt.%); a further increase in x_tot leads to the precipitation of carbon as Fe₃C. The observed presence of an amorphous structure in 19.4 at.% C (4.90 wt.%) alloy is ascribed to a deformation-driven amorphization of Fe₃C by severe plastic deformation. By measuring the temperature dependence of the grain size for an alloy with 1.77 at.% C additional evidence is provided for a metastable equilibrium reached in the nanocrystalline alloy.     

Peculiar size effect in nanocrystalline BaTiO3

Dense BaTiO₃ ceramics with grain sizes of 35 nm to 5.6 μm were prepared, and the electrical properties investigated in the temperature range 500–700 °C by means of impedance spectroscopy. Charge carriers (oxygen vacancies and holes) are depleted in the space charge regions at the BaTiO₃ grain boundaries. When the grain size is ?250 nm, the width of the space charge region was determined to be ～40 nm. Therefore, the depletion regions were expected to overlap when the grain size decreases to 35 nm; in such a situation, charge carriers would be depleted over the entire grain, resulting in depressed conductivity. However, the conductivity of the 35 nm grain size sample was measured to be one to two orders of magnitude higher than those of the microcrystalline samples, and the activation energy markedly lower. Moreover, we determined a width of ～7 nm for the space charge regions in the 35 nm grain size sample; therefore, the space charge regions do not overlap. The enhanced conductivity is ascribed to a reduced oxidation enthalpy in nanocrystalline BaTiO₃, and the distorted grain boundaries in nanocrystalline BaTiO₃ are believed to be the atomic level origin of the reduced oxidation enthalpy.     

A phenomenological study of the incomplete grain evolution in a deformed vanadium alloy

The dynamic recrystallization (DRX) behavior of a V-5Cr-5Ti (wt%) alloy was studied with a view to optimizing its hot working behavior. Uniaxial compression tests were performed over the temperature range 1373 to 1673 K and strain rate range 0.001 to 1.0 s^− 1 and the microstructural changes were examined by EBSD. Discontinuous dynamic recrystallization (d-DRX) was observed to take place in addition to continuous dynamic recrystallization (c-DRX) despite the bcc nature of this alloy. The new grains nucleated at triple junctions and along grain boundaries to form a necklace structure. Some DRX grains formed within shear bands and deformation bands as well as in the matrix when the Zener-Hollomon (Z) parameter and the strain were increased. The critical stresses and strains increased with Z while the DRX grain size decreased with Z.