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.     

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.     

Grain-size effect on plastic flow in nanocrystalline cobalt by atomistic simulation

Molecular dynamics simulation is employed to investigate the plastic flows in nanocrystalline (nc) hexagonal close-packed cobalt under uniaxial tensile deformation. In nc-Co samples modeled by a semi-empirical tight-binding potential, different deformation behaviors such as nucleation and growth of disordered atom segments (DAS) inside grains, deformation-induced hexagonal close-packed to faced-centered cubic transformation, partial dislocation activities are identified at different grain sizes (4–12 nm). At high stresses (1.2–3.2 GPa) and low temperatures (77–470 K), growth of DAS and their interaction with stacking faults are found to dominate the deformation process, even when the grain size is as small as 4 nm. A model for plastic flow generated by DAS inside grains is proposed. The strain rates and the inverse Hall–Petch-like behaviors in nc-Co with sub-10 nm grain sizes can be well described by the DAS plastic-flow model.     

In situ TEM study of microplasticity and Bauschinger effect in nanocrystalline metals

In situ transmission electron microscopy straining experiments with concurrent macroscopic stress–strain measurements were performed to study the effect of microstructural heterogeneity on the deformation behavior of nanocrystalline metal films. In microstructurally heterogeneous gold films (mean grain size d_m = 70 nm) comprising randomly oriented grains, dislocation activity is confined to relatively larger grains, with smaller grains deforming elastically, even at applied strains approaching 1.2%. This extended microplasticity leads to build-up of internal stresses, inducing a large Bauschinger effect during unloading. Microstructurally heterogeneous aluminum films (d_m = 140 nm) also show similar behavior. In contrast, microstructurally homogeneous aluminum films comprising mainly two grain families, both favorably oriented for dislocation glide, show limited microplastic deformation and minimal Bauschinger effect despite having a comparable mean grain size (d_m = 120 nm). A simple model is proposed to describe these observations. Overall, our results emphasize the need to consider both microstructural size and heterogeneity in modeling the mechanical behavior of nanocrystalline metals.     

Effects of residual S on Kirkendall void formation at Cu/Sn–3.5Ag solder joints

Solder joints of Cu/Sn–3.5Ag were prepared using Cu foil or electroplated Cu films with or without SPS additive. With a high level of SPS in the Cu electroplating bath, voids tended to localize at the Cu/Cu₃Sn interface during subsequent aging at 150 °C, which was highly detrimental to the drop impact resistance of the solder joints. In situ Auger electron spectroscopy of fractured joints revealed S segregation on the Cu/Cu₃Sn interface and void surfaces, suggesting that segregation of S to the Cu/Cu₃Sn interface lowered interface energy and thereby the free energy barrier for Kirkendall void nucleation. Once nucleated, voids can grow by local tensile stress, originating from residual stress in the film and/or the Kirkendall effect. Vacancy annihilation at the Cu/Cu₃Sn interface can induce tensile stress which drives the Kirkendall void growth.     

Deformation twins and related softening behavior in nanocrystalline Cu–30% Zn alloy

Nanocrystalline Cu–30% Zn samples were produced by high energy ball milling at 77 K and room temperature. Cryomilled flakes were further processed by ultrahigh strain high pressure torsion (HPT) or room temperature milling to produce bulk artifact-free samples. Deformation-induced grain growth and a reduction in twin probability were observed in HPT consolidated samples. Investigations of the mechanical properties by hardness measurements and tensile tests revealed that at small grain sizes of less than ～35 nm Cu–30% Zn deviates from the classical Hall–Petch relation and the strength of nanocrsytalline Cu–30% Zn is comparable with that of nanocrystalline pure copper. High resolution transmission electron microscopy studies show a high density of finely spaced deformation nanotwins, formed due to the low stacking fault energy of 14 mJ m^–2 and low temperature severe plastic deformation. Possible softening mechanisms proposed in the literature for nanotwin copper are addressed and the twin-related softening behavior in nanotwinned Cu is extended to the Cu–30% Zn alloy based on detwinning mechanisms.     

Grain growth inhibition in thin nanocrystalline Au films by grain boundary diffusion and oxidation of Ti

We studied grain growth in thin nanocrystalline Au films deposited on a sapphire substrate with and without an ultrathin Ti underlayer (adhesion promoter). The samples were annealed at 200 °C for 2 h in air. The reference thin Au film without a Ti underlayer exhibited significant grain growth during annealing, whereas no changes in microstructure of the Au layer were observed in the Au/Ti bilayers. This stabilization of the microstructure of the Au layer was attributed to thermal grain boundary grooves on the Au surface filled with Ti oxide. The grooves exhibited an elongated morphology characterized by a low apparent dihedral angle value, atypical for thermal grain boundary grooves in pure metals. We demonstrated that grooves with this morphology are very efficient in pinning grain boundary motion. We also developed a quantitative model of grain boundary grooving coupled with grain boundary interdiffusion in thin bilayer films. The model predicted the formation of long, narrow grooves at the grain boundaries, which are very efficient in suppressing grain growth in nanocrystalline thin films.     

Void growth in metals: Atomistic calculations

Molecular dynamics simulations in monocrystalline and bicrystalline copper were carried out with LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) to reveal void growth mechanisms. The specimens were subjected to tensile uniaxial strains; the results confirm that the emission of (shear) loops is the primary mechanism of void growth. It is observed that many of these shear loops develop along two slip planes (and not one, as previously thought), in a heretofore unidentified mechanism of cooperative growth. The emission of dislocations from voids is the first stage, and their reaction and interaction is the second stage. These loops, forming initially on different {1 1 1} planes, join at the intersection, if the Burgers vector of the dislocations is parallel to the intersection of two {1 1 1} planes: a 〈1 1 0〉 direction. Thus, the two dislocations cancel at the intersection and a biplanar shear loop is formed. The expansion of the loops and their cross slip leads to the severely work-hardened region surrounding a growing void. Calculations were carried out on voids with different sizes, and a size dependence of the stress threshold to emit dislocations was obtained by MD, in disagreement with the Gurson model which is scale independent. This disagreement is most marked for the nanometer sized voids. The scale dependence of the stress required to grow voids is interpreted in terms of the decreasing availability of optimally oriented shear planes and increased stress required to nucleate shear loops as the void size is reduced. The growth of voids simulated by MD is compared with the Cocks–Ashby constitutive model and significant agreement is found. The density of geometrically necessary dislocations as a function of void size is calculated based on the emission of shear loops and their outward propagation. Calculations are also carried out for a void at the interface between two grains to simulate polycrystalline response. The dislocation emission pattern is qualitatively similar to microscope observations.     

Temperature dependent tensile and fracture behaviors of Mo–10 wt.% Cu composite

Uniaxial tension tests are carried out for the Mo–10 wt.% Cu (Mo–10Cu) composite under a scanning electron microscope (SEM) at a temperature range from 25 °C to 725 °C. The stress–strain curves are obtained with both the tensile strength and the fracture strain peaked at 500 °C. Further raise of temperature would reduce the tensile strength and the fracture strain. In-situ SEM observations reveal the microstructure characteristics for Mo–10Cu composite at different temperatures. The fracture is of brittle inter-granular type when uni-axially tensioned at room temperature. As the temperature increases, formation of slip bands and linkage of micro-voids via plastic shear are observed. The fracture is characterized by mixed inter-granular fracture and plastic shear. The fracture is of predominantly plastic shear when uni-axially tensioned at 500 °C. Under uniaxial tension at temperatures higher than 650 °C, Mo–10Cu composite embrittles due to the insolubility of molybdenum and copper, and the activated grain boundary diffusion of Cu. These results are of importance for the basic understanding of the microstructure–mechanical properties relationship, as well as for the evaluation of Mo–Cu composites in practical applications.     

Effects of sulfide-forming element additions on the Kirkendall void formation and drop impact reliability of Cu/Sn–3.5Ag solder joints

Ternary Pb-free solders, Sn–3.5Ag–X, containing 0.5 wt.% of Zn, Mn and Cr, were reacted with Cu UBM, which was electroplated using SPS additive. Characteristics of Cu–Sn IMCs and Kirkendall void formation at the Cu/Sn–3.5Ag solder joints were significantly affected by the third element, and the potency to suppress Kirkendall voids at the solder joint increased in the order of Cr, Mn, Zn, which was indeed the order of the drop reliability improvement. From the AES analyses, it was suggested that the sulfide-forming elements in the solder diffused into the Cu UBM and reduced the segregation of S atoms to the Cu/Cu₃Sn interface by scavenging S, which led to the suppression of Kirkendall void nucleation at the Cu/Cu₃Sn interface and the drop reliability improvement. In the case of the Zn-containing solder joint, Cu₃Sn phase, known to be a host of Kirkendall voids, did not form at all even after extended aging treatments. The magnitude of the tensile stress at the Cu₃Sn/Cu interface which drove the Kirkendall void growth was estimated to be 10–100 MPa.     

Inelastic deformation of nanocrystalline Au thin films as a function of temperature and strain rate

The mechanical behavior of nanocrystalline Au thin films with average grain size of 64 nm was investigated at strain rates 10^?5–10 s^?1, and temperatures between 298 and 383 K. The yield strength was highly sensitive to both temperature and strain rate: at room temperature it increased by ～100% within the range of applied strain rates, while it decreased by as much as 50% in the given temperature range at each strain rate. The ductility and activation volume trends pointed to two distinct regimes of plastic deformation: namely, creep-driven and dislocation-mediated plasticity, with the transition occurring at increasing strain rate for increasing temperature. The activation volume for creep-influenced deformation increased monotonically from 6.4b³ to 29.5b³ between 298 and 383 K, signifying grain boundary (GB) diffusion processes and dislocation-mediated creep, respectively. Dislocation climb, as an accommodation mechanism for GB sliding, provided an explanation for the increased activation volume at higher temperatures. The activation volumes calculated at high strain rates decreased from 19.7b³ to 11.4b³ between 298 and 383 K. A model for thermally activated dislocation depinning was applied to explain this abnormal decreasing trend in the activation volume, resulting in activation energy of 1.2 eV.     

A new parameter for modelling three-dimensional damage evolution validated by synchrotron tomography

Novel methods of correlating damage evolution measurement techniques are explored to produce improved constitutive equations that better account for the effect of initial inclusion distributions on damage softening behaviour. Based on ex situ, high resolution, synchrotron tomographic quantification of the three-dimensional interactions of damage formed during hot deformation of free cutting steel, a new parameter to account for the effect of inclusions on damage is proposed. Uniaxial tensile samples deformed at 1100 °C and a strain rate of 0.1 s^?1 were interrupted at various strains prior to failure. Ex situ synchrotron X-ray computed tomography (sCT) was then used to quantify the growth of damage in the hot deformation of a leaded free cutting steel. Void growth is related to nucleated microvoids at inclusions. The number and volume fraction of voids were calculated for each tensile sample, allowing quantification of the evolving ductile damage via the measured increase in average void diameter after each strain increment. The equivalent diameter, spacing and volume fraction of inclusions were measured at the different interrupt strains. The local strain and stress state, evaluated using the finite element method at the microscale, were related to the local void populations. There was evidence that after necking the damage localized due to clustered inclusions. Damage localization was confirmed with a three-dimensional micromechanics model of 100 inclusions, whose distribution was taken directly from the sCT results, and a novel approach to extract the damage fraction is presented. A new parameter was introduced to account for inclusion size, spacing and clustering, which was validated against the sCT results.     

Mechanical behavior of nanoscale Cu/PdSi multilayers

Berkovich nanoindentation and uniaxial microcompression tests have been performed on sputter-deposited crystalline Cu/amorphous Pd_0.77Si_0.23 multilayered films with individual layer thicknesses ranging from 10 to 120 nm. Elastic moduli, strengths and deformation morphologies have been compared for all samples to identify trends with layer thicknesses and volume fractions. The multilayer films have strengths on the order of 2 GPa, from which Cu layer strengths on the order of 2 GPa can be inferred. The high strength is attributed to extraordinarily high strain hardening in the polycrystalline Cu layers through the inhibition of dislocation annihilation or transmission at the crystalline/amorphous interfaces. Cross-sectional microscopy shows uniform deformation within the layers, the absence of delamination at the interfaces, and folding and rotation of layers to form interlayer shear bands. Shear bands form where shear stresses are present parallel to the interfaces and involve tensile plastic strains as large as 85% without rupture of the layers. The homogeneous deformation and high strains to failure are attributed to load sharing between the amorphous and polycrystalline layers and the inhibition of strain localization within the layers.     

Microstructure evolution during dewetting in thin Au films

Thin metal films can degrade into particles in a process known as dewetting. Dewetting proceeds in several stages, including void initiation, void growth and void coalescence. Branched void growth in thin Au films was studied by means of electron backscatter diffraction (EBSD). The holes were found to protrude into the film predominantly at high angle grain boundaries and the branched shape of the holes can be explained by surface energy minimization of the grains at the void boundaries. (1 1 1) Texture sharpening during dewetting was observed and quantified by EBSD and in situ X-ray studies.     

Microstructural evolution and strain hardening of Fe–24Mn and Fe–30Mn alloys during tensile deformation

High Mn steels demonstrate an exceptional combination of high strength and ductility owing to their sustained high work hardening rate during deformation. In the present work, the microstructural evolution and work hardening of Fe–30Mn and Fe–24Mn alloys during uniaxial tensile testing at 293 K and 77 K were investigated. The Fe–30Mn alloy did not undergo significant strain-induced phase transformations or twinning during deformation at 293 K, whereas these transformations were observed during deformation at 77 K. A modified Kocks–Mecking model was successfully applied to describe the strain hardening behavior of Fe–30Mn at both temperatures, and quantitatively identified the influence of stacking fault energy and strain-induced phase transformations on dynamic recovery. The Fe–24Mn alloy underwent extensive ε martensite transformation during deformation at both test temperatures. An analytical micromechanical model was successfully used to describe the work hardening of Fe–24Mn and permitted the calculation of the ε martensite stress–strain curve and tensile properties.     

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.     

Structure and phase formation in Cu–Mn alloy thin films deposited at room temperature

Transmission electron microscopy characterization of Cu–Mn alloy thin films deposited by DC magnetron sputtering is applied to reveal the formation of phases throughout the composition range. Pure Cu and Mn films exhibit face-centred cubic (fcc) Cu and α-Mn phases, respectively. At room temperature the low Mn content films have fcc structure (γ-phase). Mn can substitute Cu in the fcc Cu lattice up to ～35 at.% Mn. The lattice parameter of fcc Cu–Mn alloy films follows a linear relationship of a₀ = a_Cu + 0.322c (in Å), where a_Cu = 3.615 Å is the lattice parameter of Cu and c is the Mn atomic concentration. At high Mn content, above 50 at.% Mn, a homogeneous one-phase structure is observed, possessing the short-range order of α-Mn. The incorporation of Cu into Mn suggests that this structure changes from crystalline α-Mn to disordered structure as the Cu content increases. A narrow two-phase region exists between 35 and 45 at.% Mn. A grain size minimum of 2–3 nm was observed in the 35–65 at.% Mn region.     

Strain rate sensitivity of nanocrystalline Au films at room temperature

The effect of strain rate on the inelastic properties of nanocrystalline Au films was quantified with 0.85 and 1.76 μm free-standing microscale tension specimens tested over eight decades of strain rate, between 6 × 10^?6 and 20 s^?1. The elastic modulus was independent of the strain rate, 66 ± 4.5 GPa, but the inelastic mechanical response was clearly rate sensitive. The yield strength and the ultimate tensile strength increased with the strain rate in the ranges 575–895 MPa and 675–940 MPa, respectively, with the yield strength reaching the tensile strength at strain rates faster than 10^?1 s^?1. The activation volumes for the two film thicknesses were 4.5 and 8.1 b³, at strain rates smaller than 10^?4 s^?1 and 12.5 and 14.6 b³ at strain rates higher than 10^?4 s^?1, while the strain rate sensitivity factor and the ultimate tensile strain increased below 10^?4 s^?1. The latter trends indicated that the strain rate regime 10^?5–10^?4 s^?1 is pivotal in the mechanical response of the particular nanocrystalline Au films. The increased rate sensitivity and the reduced activation volume at slow strain rates were attributed to grain boundary processes that also led to prolonged (5–6 h) and significant primary creep with initial strain rate of the order of 10^?7 s^?1.     

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.     

含孔洞的Al2Cu单轴拉伸的分子动力学模拟

建立含孔洞的Al₂Cu分子动力学模拟模型,采用嵌入原子法模拟Al₂Cu模型在常温、恒定工程应变速率的拉伸环境下孔洞大小、数量及孔洞分布对Al₂Cu力学性能的影响。研究结果表明：孔洞的出现使模型内部出现了自由表面并在孔洞内边缘产生了应力集中,从而大大降低材料的抗拉强度以及变形能力;孔洞增大,Al₂Cu的塑性和抗拉强度均明显下降;不同孔洞数量对应的应力应变曲线在弹性变形阶段基本重合,孔洞增多,Al₂Cu的塑性以及抗拉强度都有不同程度的下降;改变孔洞分布,孔洞连线方向与拉伸方向的夹角越小,Al₂Cu表现出越强的塑性和抗拉强度。