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Coarsening of solder microstructures dramatically affects fatigue lifetimes. This paper presents a study of microstructural evolution due to thermal cycling and aging of small solder joints.

Using pseudopotential density functional theory within the local-density approximation, we calculate the ideal shear strengths of W for slip on {110}, {112} and {123} planes allowing for complete structural relaxation orthogonal to the applied shear. The strengths in the weak directions on all planes are found to be very nearly equal (about 18GPa, or 11% of the shear modulus G). Moreover, the shear instability occurs at approximately the same applied shear strain (17–18%). This unusual isotropy is explained in terms of the atomic configurations of high-energy saddle points reached during shear. Analysis of these saddle points may also offer a simple explanation for the prevalence of the pencil glide of dislocations on planes containing a (111) direction in bcc metals. Finally, we calculate the ideal cleavage strengths of W on {100} and compare our calculated ideal shear and cleavage strengths with experimental nanoindentation and whisker measurements. All these results can be rather simply unders...

Recent work has shown that a Au−Ni−Sn ternary compound with a nominal composition of Au0.5Ni0.5Sn4 redeposits and grows at the interface between eutectic Pb−Sn solder and Ni/Au metallization during aging at 150°C. The present work verifies the existence of the Au0.5Ni0.5Sn4 phase by examining the Sn-rich corner of the Au−Ni−Sn ternary phase diagram. The reconfiguration mechanism of the AuSn4 from the bulk solder is also discussed, with detailed observations of the Au0.5Ni0.5Sn4 microstructure. The results show that the Ni solubility limit in the AuSn4 phase is approximately 12 at.% at 150°C and thus, the Au0.5Ni0.5Sn4 phase is a ternary AuSn4-based compound with high Ni solubility. Due to the slight solubility and the fast diffusion of Au in the eutectic Pb−Sn at 150°C, the AuSn4 intermetallics in the bulk solder can reconfigure to form a AuxNi1−xSn4 compound at the interface where Ni is available. The AuxNi1−xSn4 compound layer consists of nanocrystals arranged in a larger grainlike morphology. It appears that the inherent lattice strain of the AuxNi1−xSn4 compound and the volume change due to its formation results in a nanocrystalline microstructure.

Scanning SQUID microscopy is shown to be capable of detecting deformation gradients when accompanied by significant changes in hardness. Deformation which does not increase the dislocation density (as measured by the increase in hardness) has little effect. The effect can be produced by different techniques including cold rolling and tensile deformation. The effect is shown to occur in at least two different alloys with very different microstructures indicating the possibility of wide applicability.

The principal focus of this work is to explain precipitation in Al–1 at.%Si–1at%Ge. The microstructure is characterized using conventional and high resolution transmission electron microscopy, as well as energy dispersive X-ray spectroscopy. The first precipitates to come out of solid solution have a cube–cube orientation relationship with the matrix. High resolution TEM demonstrated that all the precipitates start out, and remain multiply twinned throughout the aging treatment. Any twinned section of the precipitate no longer maintains a low index interface with the matrix, and consequently goes from a crystallographic to a spherical interface with the matrix. This explains the equiaxed shape of the Si–Ge precipitates. There is a variation in the stoichiometry of the precipitates, with the mean composition being Si–44.5 at.%Ge. It is also shown that in Al–Si–Ge it is not possible to achieve satisfactory hardness through conventional heat treatment. This result is explained in terms of sluggish precipitation of the diamond-cubic Si–Ge phase coupled with particle coarsening.

Superconducting quantum interference device (SQUID) microscopes may serve as useful nondestructive evaluation (NDE) tools since they can precisely measure the local magnetic field variation that can be related to the characteristics of ferromagnetic materials. To demonstrate this, we have studied magnetic functionally graded materials (FGMs) in the Fe–Cr–Ni alloy system using a high-transition-temperature (HTc) SQUID microscope. The FGMs were either fabricated by inhomogeneous mechanical deformation or by heat treatment in a temperature gradient. The magnetic properties of these materials were measured using the vibrating sample magnetometer technique along the deformation or the temperature gradients. The results from this technique and the microstructural properties from optical imaging are discussed in conjunction with the magnetic field images obtained from the SQUID microscope. By exploring the results, the feasibility and benefit of utilizing SQUID microscopy as a NDE tool are discussed.

improve shape removal and reduce internal stress remove the incoming defect, is dependent upon the number levels. However, residual stresses and specifically and diameter of bending rolls (workstations) employed. In the imbalance of these stresses post-levelling is an pure stretch levelling no specific bending rolls are used. issue that has failed to be addressed in its entirety. High tensions, therefore, must be generated as a result of To investigate the generation and effects of residual considerable velocity differentials at large diameter bridle stresses owing to tension levelling, a finite element drums. Consequently, this can lead to plastic instabilities (FE) model has been developed with validation

The ideal structural steel combines high strength with excellent fracture toughness. In this paper we consider the limits of strength and toughness from two perspectives. The first perspective is theoretical. It has recently become possible to compute the ideal shear and tensile strengths of defect-free crystals. While the ferromagnetism of bcc Fe makes it a particularly difficult problem, we can estimate its limiting properties from those of similar materials. The expected behavior at the limit of strength contains many familiar features, including cleavage on {100}, slip on multiple planes, "conditionally" brittle behavior at low temperature and a trend away from brittle behavior on alloying with Ni. The behavior of fcc materials at the limit of strength suggests that true cleavage will not happen in austenitic steels. The results predict an ideal cleavage stress near 10.5 GPa, and a shear strength near 6.5 GPa. The second perspective is practical: how to maximize the toughness of high-strength steel. Our discussion here is limited to the subtopic that has been the focus of research in our own group: the use of thermal treatments to inhibit transgranular brittle fracture in lath martensitic steels. The central purpose of the heat treatments described here is grain refinement, and the objective of grain refinement is to limit the crystallographic coherence length for transgranular crack propagation. There are two important sources of transgranular embrittlement: thermal (or, more properly, mechanical) embrittlement at the ductile–brittle transition, and hydrogen embrittlement from improper heat treatment or environmental attack. As we shall discuss, these embrittling mechanisms use different crack paths in lath martensitic steels and, therefore, call for somewhat different remedies.

This paper investigates the conditions of elastic stability that set the upper limits of mechanical strength. Following Gibbs, we determine the conditions that ensure stability against reconfigurations that leave the boundary of the system unchanged. The results hold independent of the nature of properties of the loading mechanisms but are identical with those derived previously for a solid in contact with a reservoir that maintains the Cauchy stress. Mechanisms that control the stress in some other way may add further conditions of stability; nonetheless, the conditions of internal stability must always be obeyed and can be consistently used to define the ultimate strength. The conditions of stability are contained in the requirement that λ ijkl δe ij δe kl ≥ 0 for all infinitesimal strains, where λ ijkl = 1/2(B ijkl + B klij ), and B is the tensor that governs the change in the Cauchy stress t during incremental strain from a stressed state τ: t ij = T ij + B ijkl δe kl . Since λ has full Voigt symmetry, it can be written as the 6 x 6 matrix λ ij with eigenvalues λ α . Stability is lost when the least of these vanishes. The conditions of stability are exhibited for cubic (hydrostatic), tetragonal (tensile) and monoclinic (shear) distortions of a cubic crystal and some of their implications are discussed. Elastic stability and the limits of strength are now being explored through first-principles calculations that increment uniaxial stretch or shear to find the maximum stress. We discuss the nature of this limiting stress and the steps that may be taken to identify orthogonal instabilities that might intrude before it is reached.

The work reported here concerns the effect of Si on the precipitation of θ′ phase (metastable Al2Cu) during the isothermal aging of Al-2Cu-1 Si (wt pct). The binary alloys Al-2Cu and Al-1 Si were studied for comparison. Only two precipitate phases were detected: essentially pure Si in Al-1 Si and Al-2Cu-1 Si, and θ′ (metastable Al2Cu) in Al-2Cu and Al-2Cu-1Si. On aging the ternary alloy at 225 °C, Si precipitates first and catalyzes the θ′ phase. The precipitates in the ternary alloy are smaller, are more densely distributed, have lower aspect ratios, and coarsen more slowly than those in the binary Al-2Cu aged at the same temperature. While the shapes of individual θ′ precipitates in binary Al-2Cu are strongly affected by the kinetic problem of nucleating growth ledges, which produces a significant scatter in the aspect ratio for samples of given thickness, the overall evolution of particle shape with size follows the predictions of the Khachaturyan-Hairapetyan (KH) thermoelastic theory, which reduces to κ=L/d ∞ √L at large sizes. The KH theory provides an estimate for the interfacial tension of the broad Al-θ′ interface of 85 to 96 mJ/m2, which is near the values for other low-energy interfaces in Al, such as the twin boundary energy (100 mJ/m2) and the antiphase boundary energy in δ′ Al3Li (70 mJ/m2). Si and θ′ precipitates in Al-2Cu-1 Si have a strong elastic interaction because of their compensating strain fields. This elastic interaction promotes the nucleation of θ′ precipitates on Si, decreases the expected aspect ratio of θ′, and inhibits coarsening. Finally, Si precipitation in ternary Al-2Cu-1 Si differs from that in binary Al-1 Si in that the Si precipitates are coarser, more equiaxed, and more extensively twinned. These changes appear to be effects of Cu, which increases the solubility of Si in Al and adsorbs on the Si-Al interface, promoting twinning by a “step-poisoning” effect at the interface.

Au/Ni metallization has become increasingly common in microelectronic packaging when Cu pads are joined with Pb-Sn solder. Recent work has shown that a ternary compound with stoichiometry Au0.5Ni0.5Sn4 redeposits onto the interface during aging, compromising the strength of the joint. In the present work the growth of the Au0.5Ni0.5Sn4 layer is documented and methods for inhibiting its growth were investigated. It was determined that multiple reflows, both with and without additional aging, can substantially limit the thickness of the ternary layer.

The present work studies the microstructure and microstructural evolution of small volumes of nominally eutectic Au-Sn solder on Cu. The study includes solder bumps 140–145 µm in diameter and 55–65 µm tall deposited on Cu-plated Si, and solder joints 60 µm in diameter and 25 µm in height that join Cu-plated ceramic and polymide substrates. The results show that the microstructure is strongly affected by the addition of Cu from the substrate during reflow, which produces a thick intermetallic layer along the interface. In the case of the joints, normal processing produces a coarse microstructure that includes only a few grains between thick intermetallic coatings. Aging at high temperature causes a further monotonic increase in Cu content, which alters the intermetallic structure at the interfaces and can lead to intermetallic bridging across the joint. Thermal fatigue tests suggest that cyclic deformation breaks up the intermetallic structure, increasing the rate of Cu addition to the joint, but refining the apparent grain size.

The remanent magnetization of ferromagnetic steel with five different microstructures has been studied using a microscope based on a high-transition-temperature d.c. Superconducting QUantum Interference Device (SQUID). The samples were prepared using different heat treatments, beginning with the same material composition. Each sample was magnetized in turn in a magnetic field of 50 mT, and the remanent magnetization was studied by scanning the sample over the SQUID using a two-dimensional translation stage with a range of 50×50 mm 2 . With a sample-to-SQUID separation of 400–500 μm, this procedure yielded a two-dimensional magnetic field image produced by the local remanent magnetization of the sample. In addition, microstructural information has been obtained using optical imaging, allowing the magnetic images to be correlated with the underlying microstructure.

Tension levelling is employed in cold steel strip manufacturing to guarantee that flat material is provided for shape-critical applications. The loading system of the process leads to a corresponding [very] low cycle fatigue stress–strain history being applied to surface and sub-surface sections of the material. In this paper, results are presented from a series of low cycle fatigue tests (in the crack-free phase) under constant strain amplitude control for a number of strain amplitudes, typical of those found in levelling applications. The results for the tests reported here suggest that a mixed mode work hardening process is present, with the application of a Bauschinger effect resulting in a closed hysteresis loop on completion of the first cycle. All tests showed that the material gradually work softened under the cyclic loads imposed. Strain-amplitude dependent work hardening, however, was observed in some early cycles.

There has been continued debate over the relative importance of crack closure and other sources of Kmax dependence in metallic fatigue crack growth. Crack closure is believed to be a very important physical mechanism that is a source for the observed dependence of fatigue on load ratio or Kmax. It is unclear whether the difficulty in observing some hypothesized crack closure is the result of the very small distances over which contact may occur, or whether new mechanisms which operate in front of the crack tip are affecting crack growth. From the existing experimental fatigue data, two driving force models have been developed, one based on crack closure and a ΔKeffective term, and a second based on two terms: ΔK and Kmax. We show how these two driving force models are mathematically compatible with each other, examine what these models say about microstructural mechanisms of fatigue crack growth, and discuss the implications of each model on mechanical design of structures, materials design, and materials science. If there is to be continued debate over the relative importance of closure behind the crack tip and of the effects of stresses in front of the crack tip, we believe the debate should focus on the physical micro-mechanisms involved, rather than on analysis of the mechanical driving forces of crack growth or far field estimates of crack closure.

We have studied the effects of heat treatment and mechanical stress on the remanent magnetization of ferromagnetic steels using a high-transition-temperature (HTC) Superconducting QUantum Interference Device (SQUID) microscope. Samples were prepared by different heat treatments, which produced varied microstructures, and different rolling treatments, which produced varied levels of deformation. The samples were subsequently magnetized in fields of 50 mT, and the remanent magnetization was measured by rastering the sample over the SQUID using a two-dimensional (2D) translation stage with a scanning range of 50 mm/spl times/50 mm. With a separation between the SQUID and sample of approximately 0.5 mm, this produced a 2D magnetic field image due to the local remanent magnetization of the sample. In addition, microstructural information was determined using optical imaging, allowing us to correlate the effects of heat treatment and mechanical stress on local remanent magnetisation with detailed microstructural information. Since the strength and integrity of steels can be well predicted from microstructural information, correlation of this information with the 2D remanent magnetization images could lead to an effective method for the non-destructive evaluation of ferromagnetic steels through a simple measurement of remanent magnetization.

The ideal shear strength is the minimum stress needed to plastically deform an infinite dislocation-free crystal and is an upper bound to the strength of a real crystal. We calculate the ideal shear strengths of Al and Cu at zero temperature using pseudopotential density functional theory within the local density approximation. These calculations allow for structural relaxation of all five strain components other than the imposed shear strain and result in strengths on ${111}$ planes of 1.85 and 2.65 GPa for Al and Cu, respectively ( $8%$-- $9%$ of the shear moduli). In both Al and Cu, the structural relaxations reduce the ideal shear strengths by $35%$ to $45%$, but the directions of relaxation strain in each are qualitatively different.

The addition of 3 wt.% Ag to In results in a eutectic composition with improved mechanical properties while only slightly lowering the melting temperature. Steady-state creep properties of In-Ag eutectic solder joints have been measured using constant load tests at 0, 30, 60, and 90°C. Constitutive equations are derived to describe the creep behavior. The data are well represented by an equation of the form proposed by Dorn: a power-law equation applies to each independent creep mechanism. Two parallel mechanisms were observed for the In-Ag eutectic joints. The high-stress mechanism is a bulk mechanism with a thermal dependence dominated by the thermal dependence of creep in the Inrich matrix. The low-stress mechanism is a grain boundary mechanism. Results of this work are discussed with regard to creep behavior of typical eutectic systems.

This paper reports a technique that fabricates a magnetically graded material in which the saturation magnetization varies linearly as a function of distance. An initially wedge-shaped 304 stainless steel was rolled into a rectangular cross section. The saturation magnetization curve as a function of rolling ratio has a positive curvature. Since the rolling ratio distribution showed a negative curvature, it was possible to achieve a nearly linear magnetic gradient along the specimen. Furthermore, it was found that the hardness also varied gradually in the deformed specimen, suggesting that the technique presented in this work can fabricate a functionally graded material not only in magnetic properties but also in mechanical properties.

This work was done to clarify the metallurgical mechanisms that are used in thermal treatments to refine the effective grain size of lath martensitic steels. The alloy chosen for this work was Fe–12Ni–0.25Ti, which provides a well-defined lath martensite structure in the as-quenched condition. The alloy was given four prototypic heat treatments: (1) an anneal-and-quench treatment, (2) an intercritical anneal, (3) a single or double anneal in the austenite range, and (4) a single or double reversion to austenite at a rapid heating rate. Two effective grain sizes were identified for each heat treatment: the packet size, or dimension over which adjacent martensite laths have a common crystallographic orientation, and the prior austenite grain size. The former controls the ductile–brittle transition temperature (DBTT), the latter controls intergranular embrittlement. The different heat treatments suppress the DBTT and increase resistance to intergranular embrittlement to the extent that they decrease the relevant grain size. Rapid reversion is the most successful of the heat treatments since it destroys the alignment of laths within a packet. Rapid reversion readily yields an effective grain size near 1 μm, leading to a very low ductile–brittle transition temperature and a substantial resistance to temper or hydrogen embrittlement.

Recent studies of transition metal alloys with compositions that place them near their limits of elastic stability [e.g., near the body-centered-cubic (BCC) to hexagonal-close-packed (HCP) transition] suggest interesting behavior for the dislocation cores. Specifically, the dislocation core size is predicted to diverge as the stability limit is approached. Here a simple analysis rooted in elasticity theory and the computation of ideal strength is used to analyze this divergence. This analysis indicates that dislocation core radii should diverge as the elastic limits of stability are approached in the BCC, HCP, and face-centered-cubic (FCC) structures. Moreover, external stresses and dislocation-induced stresses also increase the core radii. Density functional theory based total-energy calculations are combined with anisotropic elasticity theory to compute numerical estimates of dislocation core radii.

The effects of isothermal tempering on the coarsening behavior of hexagonal M2C precipitates and the secondary hardening reaction in ultrahigh-strength AerMet 100 steel were investigated. The tempering temperatures were 468 °C, 482 °C, and 510 °C, and the tempering time spanned the range from 1 to 400 hours. Experimental studies of the coarsening behavior of the carbides were made by utilizing transmission electron microscopy (TEM), scanning electron microscopy (SEM), and X-ray diffractometry (XRD). The hardness at the secondary hardening peak was about HRc 55. The average length and diameter of M2C carbides were 4 to 8 nm and 1.5 to 2.5 nm, respectively, at all three tempering temperatures; hence, the aspect ratio was almost 3, an equilibrium value in this case. The size of the M2C carbides increased monotonically with time, but the growth kinetics did not exactly follow the classical coarsening behavior. The amount of precipitated austenite increased with tempering time and temperature. M2C precipitates were still relatively fine even after 200 hours of tempering. This feature seemed to be closely related to the high hardness maintained after prolonged tempering.

The possibility is addressed of improving the electromigration resistance of Al and Al–Cu thin‐film conductors with ‘‘quasi‐bamboo’’ structures by post‐pattern anneals that decrease the maximum polygranular segment length. Pure Al, Al–2Cu, and Al–2Cu–1Si lines were patterned and annealed at temperatures high enough to stimulate grain growth. Appropriate anneals led to predominantly bamboo structures with short polygranular segments. These grain structures had a high median time to failure with a relatively low deviation of the time to failure. Metallographic analyses showed that polygranular segment length was a dominant factor in determining the failure site. Post‐pattern annealing promotes a preferential shortening of the relatively long polygranular segments that cause early failures. However, even after annealing, failure occurred at the longest residual polygranular segments, even when these were significantly shorter than the ‘‘Blech length’’ under the test conditions. Statistical analysis of the failure of alloy lines revealed a simple exponential relation between the failure time and the longest polygranular segment length within a line, which is functionally identical to that previously found for lines tested in the as‐patterned condition.

This article reports the results of computer simulation studies of reversible, athermal martensitic transformations in idealized, two-dimensional crystals. The transformation is accomplished by se-quentially transforming elementary cells. The model accounts for the elastic strain developed during the transformation, assuming homogeneous elastic constants, negligible interfacial tension, and no external stress. The effects of frictional resistance to the transformation and plastic relaxation of the elastic strain are included in a simple way. The model is used to study the sources of hysteresis in the temperature-transformation (TT) curve and in the microstructural transformation path when the transformation is reversed. The central result is that some hysteresis is inevitable in a transformation of the type studied here. Even in the absence of friction and plastic relaxation, the transformation follows a path in which sequential elements of martensite relax the elastic strain of those that have previously formed. This causes the martensite to form in bursts and has the consequence that the reverse transformation does not reverse the path of the forward transformation. Friction and plastic relaxation increase hysteresis.

Electromigration is a serious potential source of failure in the narrow, thin-film Al-Cu conductors used in modern microelectronic devices. The problem has become more acute as line widths have shrunk to below one micrometer, creating lines with quasi-bamboo microstructures. The usual mechanism of internal electromigration failure in such lines involves the formation of a transgranular void across a bamboo grain at the upstream end of a long, polygranular segment, preceded by the depletion of copper from both the polygranular segment and the upstream bamboo grain. At least three metallurgical mechanisms are available to inhibit this failure mechanism and improve the useful lifetime of the line, Each of these methods has been demonstrated in the laboratory environment.

The work reported here concerns the effect of a brief exposure to a reversed current on the electromigration failure of narrow Al-Cu thin-film conducting lines. While the precise mechanism by which Cu retards electromigration in AlCu alloys is not fully understood, the consistent observation that electromigration failure is preceded by the sweeping of Cu from the failure site can be used to improve electromigration resistance by stabilizing the distribution of Cu. One way of doing this is to expose the Al-Cu line to a reverse current for some period of time. The present work shows that this method is particularly effective in thin lines with “quasi-bamboo” microstructures. It has the effect of building a reservoir of Cu at the upstream ends of the polygranular segments that are the preferred failure sites, and significantly increases both the mean time to failure, and the time to first failure of a distribution of lines. It can be inferred from these results that Al-Cu lines that conduct alternating current should be exceptionally resistant to electromigration failure.

In this paper we discuss the microstructure of lath martensitic steels and the mechanisms by which it controls cleavage fracture. The specific experimental example is a 9Ni (9 wt% Ni) steel annealed to have a large prior austenite grain size, then examined and tested in the as-quenched condition to produce a relatively coarse lath martensite. The microstructure is shown to approximate the recently identified 'classic' lath martensite structure: prior austenite grains are divided into packets, packets are subdivided into blocks, and blocks contain interleaved laths whose variants are the two Kurjumov-Sachs relations that share the same Bain axis of the transformation. When the steel is fractured in brittle cleavage, the laths in the block share {100} cleavage planes and cleave as a unit. However, cleavage cracks deflect or blunt at the boundaries between blocks with different Bain axes. It follows that, as predicted, the block size governs the effective grain size for cleavage.

Wettability of pretinned Cu decreases after long aging times. This work provides insight into the role Cu-Sn intermetallics play in wettability degradation. This study investigates the effects of aging in air and argon at 170°C on Cu coupons which were pretinned with 75Sn-25Pb solder. Coating was applied using an electroplating technique. The coating thickness was controlled between 3 to 30 μm and the specimens were aged for 0, 2, 24 h, and two weeks. Wetting balance tests were used to evaluate the wettability of the test specimens. Microstructural development was evaluated using x-ray diffraction, energy dispersive x-ray, and Auger spectroscopy, as well as optical and scanning electron microscopy. Results indicate that Cu-Sn intermetallics protected from oxidation do not contribute to a decrease in wettability. Oxidized intermetallics, however, significantly de-crease the wettability of aged pretinned samples. The extent of degradation is determined by the type of oxide formed on the surface of the intermetallic. This study shows that a predominantly Cu oxide forms on Cu3Sn, while a Sn oxide forms on Cu6Sn5. No evidence of internal oxidation was found.

This article reports research on the initiation and growth of small fatigue cracks in a nickel-base superalloy (produced commercially by INCO as INCOLOY* 908) at 298 and 77 K. The experimental samples were square-bar specimens with polished surfaces, loaded in fourpoint bending. The crack initiation sites, crack growth rates, and microstructural crack paths were determined, as was the large-crack growth behavior, both at constant load ratio (R) and at constant maximum stress intensity (Kmax). Small surface cracks initiated predominantly at (Nb,Ti)xCy, inclusion particles, and, less frequently, at grain boundaries. Small cracks grew predominantly along {111} planes in individual grains and were perturbed or arrested at grain boundaries. For values of ΔK above the large-crack threshold, ΔKth, the average rate of smallcrack growth was reasonably close to that of large cracks tested under closure-free conditions. However, short-crack growth rates varied widely, reflecting the local heterogeneity of the microstructure. The threshold cyclic stress (Δσth) and the threshold cyclic stress intensity (ΔKσth) for small surface cracks were measured as functions of the crack size, 2c. The results suggest that a combination of the fatigue endurance limit and the threshold stress intensity for closure-free growth of large cracks can be used to define a fatigue-safe load regime.

The stability of competing phases within body-centered-cubic Ti-V approximants to gum metal is considered from the perspective of phonon dispersion. Phonons are associated with the potential to form the $\ensuremath{\omega}$ and ${\ensuremath{\alpha}}^{\ensuremath{'}\ensuremath{'}}$ phases. It is argued that alloys can be designed to be linearly stable with respect to the formation of both phases, even as the ideal shear strength approaches zero. The reduction in ideal strength is associated with softening of the phonons along $\ensuremath{\Gamma}\ensuremath{-}N$ and is reflected in diffuse-scattering diffraction experiments.

This work addresses cell formation from an initially homogeneous distribution of parallel edge dislocations. We consider an array of interacting, nearly parallel edge dislocations that glide on a single plane, but may also climb. We obtain a set of nonlinear differential equations that describe the evolution of the dislocation distribution, and find the instability conditions that lead toward cells. Three particularly interesting results emerge. First, the distribution of edge dislocations is always at least mathematically unstable with respect to cell formation when dislocations can be created or destroyed. Second, the locus of that instability is very sensitive to the efficiency of the dislocation creation mechanisms. Third, both relatively equiaxed and highly elongated cells may form, depending on the temperature and the ratio of the stresses that drive glide and climb.

This study was conducted in order to determine and understand the effect of substrate on the behavior of eutectic In-Sn. Samples for mechanical testing were produced with either bare Cu or Ni on Cu substrates. Both the microstructure and the mechanical behavior are strongly dependent on substrate. When eutectic In-Sn is joined to bare Cu, Cu diffusion into the joint causes the alloy to become off-eutectic, giving a nonuniform and irregular microstructure. The addition of a layer of Ni acts as a diffusion barrier, preventing Cu diffusion sufficiently such that a uniform, normal colony-based eutectic forms. Deformation is more uniform in the In-Sn on Ni, while it is concentrated along the length of the joint in the In-Sn on Cu. This distinction is reflected in the different shapes of shear stress-strain curves between In-Sn on Cu and In-Sn on Ni. The stress exponents and activation energies for creep also vary with substrate. Creep deformation is governed by the In-rich β phase for In-Sn on Cu and by the Sn-rich γ phase for In-Sn on Ni. If In-Sn on Ni samples are aged, the microstructure coarsens and the mechanical behavior changes to resemble that of the as-cast In-Sn on Cu.

Conducting joints with low fabrication temperatures and high thermal stability are useful in modern electronics. This paper discusses the potential use of intermetallic phases in making such joints. Thin interconnection layers that consist entirely of intermetallic phases have been produced by joining planar Cu substrates that are coated with thin films of Sn. Thin layers (1-5 µm) of intermetallic phase are produced at temperatures slightly above the melting temperature of Sn in a process similar to reflow soldering. Metallography and x-ray analysis are used to characterize the formation mechanism of the intermetallic. Cu dissolves into the liquid Sn by diffusion along narrow channels between grains of the growing η-Cu6Sn6 intermetallic phase. Tensile tests were used to measure mechanical properties. The joint strength increased with reaction time. The joint fails in a ductile mode as long as unreacted Sn is present, but fractures along interphase boundaries when the joint is completely intermetallic.

Gold plating is used in the microelectronics industry to maintain the wettability of metal substrates. The nature of wetting during soldering of gold plated metals is discussed, and the results of experiments on the fluxless wettability and oxidation of gold plated nickel are described. The results suggest that electrodeposition of a thin gold plate (0.14 (xm) and the concurrent reduction of nickel oxide produce a gold-nickel system which will wet without flux. Oxidation of nickel was observed to occur via nickel out-diffusion and by direct exposure of the substrate through pinhole plating defects. Auger chemical analysis indicates that pinholes do not produce oxidation of the surrounding substrate area.

The effects of low Au concentrations on the creep properties of a eutectic Sn/Pb alloy were investigated. Creep testing was performed on double-shear specimens of fine-grained, eutectic Sn/Pb joints with Au concentrations of 0, 0.2, 1.0, and 1.5 wt pct Au at 90 °C, 0, 0.2, and 1.0 wt pct Au at 65°C, and 0.2 wt pct Au at 25 °C. In the absence of Au, the creep of finegrained eutectic Sn/Pb is dominated by grain-boundary sliding at high homologous temperature and intermediate stress. The addition of 0.2 wt pct Au or more suppressed this mechanism; the high-stress, bulk-creep mechanism was dominant at all stresses tested. Higher concentrations of Au increased porosity within the joints. The porosity decreased joint strength. During failure, the crack path followed softer regions of the joint; cracks propagated through Pb-rich islands or along Sn/Sn grain boundaries.

Eutectic Bi-Sn and In-Sn solder joints were subjected to high temperature deformation in shear in order to determine whether microstructural instabilities are generated during testing. Dynamic recrystallization had previously been observed in Sn-Pb solder joints during creep and fatigue in shear. The current study shows that Bi-Sn can recrystallize during deformation in creep or at constant strain rate, whereas no microstructural changes are observed in In-Sn. Recrystallization of Bi-Sn is concentrated in a narrow band along the length of the sample, parallel to the direction of shear strain, similar to behavior in Sn-Pb. The recrystallization appears to proceed by migration of interphase boundaries rather than by a nucleation and growth mechanism. A minimum total strain is required to induce obvious recrystallization in Bi-Sn, independent of applied stress or strain rate. This value of strain is much higher than the strain at initiation of tertiary creep or at the maximum shear stress. Onset of tertiary creep and strain softening occur as a result of nonuniform deformation in the samples that is independent of the microstructural instabilities. The creep behavior of In-Sn is relatively straightforward, with a single creep mechanism operating at all temperatures tested. The creep behavior of Bi-Sn is temperature-dependent. Two mechanisms operate at lower temperatures, but there is still some question as to whether one or both of these, or a third mechanism, operates at higher temperatures.

The rate of resistivity decay in Al‐2Cu‐1Si thin‐film conductors was studied as a function of temperature and grain size distribution. The decay kinetics were assumed to be governed by the rate of precipitate reconfiguration to grain boundaries. This assumption was confirmed by transmission electron microscopy (TEM) observations of the microstructure during resistance decay, and by studies of lines of two different widths. The results can be explained qualitatively from the microstructure of the lines. In particular, increasing the mean grain size slows the rate of resistivity decay, and establishing a bimodal distribution with a significant population of relatively large grains has the same effect. A simple model was developed to treat these effects quantitatively. The model assumes a cylindrical grain geometry and a uniform initial distribution of Cu and ignores the effect of intragranular precipitation. The model yields reasonable values for the activation energy for Cu diffusion in thin films, and pre...

This paper describes the creep behavior of three tin-rich solders that have become candidates for use in lead-free solder joints: Sn-3.5Ag, Sn-3Ag-0.5Cu, and Sn-0.7Cu. The three solders show the same general behavior when tested in thin joints between copper and Ni/Au metallized pads at temperatures between 60‡C and 130°C. Their steady-state creep rates are separated into two regimes with different stress exponents. The low-stress exponents range from ∼3–6, while the high-stress exponents are anomalously high (7–12). Strikingly, the high-stress exponent has a strong temperature dependence near room temperature, increasing significantly as the temperature drops from 95°C to 60°C. The anomalous creep behavior of the solders appears to be due to the dominant tin constituent. Research on creep in bulk samples of pure tin suggests that the anomalous temperature dependence of the stress exponent may show a change in the dominant mechanism of creep. Whatever its source, it has the consequence that conventional constitutive relations for steady-state creep must be used with caution in treating tin-rich solder joints, and qualification tests that are intended to verify performance should be carefully designed.

Fatigue cracks often initiate at surface inclusions, and sometimes appear at inclusions within the bulk. To clarify the relative efficiency of these crack sources, an approximate solution for the elastic stress of a hemispherical surface inclusion is provided and compared with the existing result of a spherical interior inclusion. The approximate solution is obtained from the Eshelby solution for the elastic field of an ellipsoid inclusion by introducing the Green's function of an elastic half-space. The numerical calculated results indicate that the stress concentration of a surface inclusion is higher when the inclusion is harder than the matrix, while that of an embedded inclusion is higher when the inclusion is softer than the matrix.

This article reports a computer simulation study of the microstructures produced by martensitic transformations. In the present work, the transformation strain is dyadic, and the transformation is athermal and irreversible. The transformation occurs in a two-dimensional crystal that is constrained in a matrix that has no net transformation strain and may be subject to external stress. The crystal is divided into elementary cells. The transformation is simulated by computing the elastic strain energy in the linear elastic approximation and transforming the most-favored cell in each step to generate the minimum-energy transformation path. The simulation generates the microstructure at each step of the transformation and plots a temperature-transformation (TT) curve by computing the chemical driving force required to maintain the transformation and assuming that it is proportional to the undercooling. The results show that the matrix constraint causes complex, multivariant microstructures and separatesMsandMf. Multiple variants partly relax the shear part of transformation strain but interfere so that the transformation is difficult to maintain. The dilational part of the transformation strain produces interesting microstructures, such as “butterfly martensite,” in partially transformed crystals. It also increases ΔM since it produces a hydrostatic stress that cannot be compensated by mixing variants. The applied stress can be divided into hydrostatic and deviatoric components. The hydrostatic component changesMswithout altering the microstructure or ΔM. The deviatoric stress changes the relative energies of the variants and produces a microstructure that is rich in the favored variant. It also increases ΔM, since single-variant transformations must be sustained against an accumulating, uncompensated shear. The thermal resistance (ΔM) increases with the magnitude of the deviatoric stress until a high-stress limit is reached and only one variant appears. The microstructure is most complex at intermediate stress, where both variants develop in a complex internal stress field. Cyclic stress dramatically increases the extent of transformation at given maximum load. The martensite that has already formed becomes a source of intense internal stress when the stress is reversed, promoting further transformation.

This work is principally concerned with the microstructure of electromigration failure in narrow Al‐2Cu‐1Si conducting lines on Si. Samples were patterned from 0.5‐μm‐thick vapor‐deposited films with mean grain size of 2.4 μm, and had linewidths of 1.3 μm (W/G≊0.5), 2 μm (W/G≊0.8), and 6 μm (W/G≊2.5). The lines were tested to failure at T=226 °C and j=2.5×106 A/cm2. Other samples were tested over a range of substrate temperatures and current densities to test the effect of these variables, and 1.3 μm lines were tested after preaging at 226 °C for various times to change the Cu‐precipitate distribution prior to testing. Three failure modes were observed: The 6 μm specimens failed by separation along grain boundaries with an apparent activation energy of 0.65 eV; the 1.3 μm specimens that were preaged for 24 h failed after very long times by gradual thinning to rupture; all other narrow lines failed by the transgranular‐slit mechanism with an activation energy near 0.93 eV. Microstructural studies suggest that the transgranular‐slit failure mechanism is due to the accumulation of a supersaturation of vacancies in the bamboo grains that terminate polygranular segments in the line. Failure occurs after Cu has been swept from the grain that fails. Failure happens first at the end of the longest polygranular segment of the line, at a time that decreases exponentially with the polygranular segment length. Preaging the line to create a more stable distribution of Cu lengthens the time required to sweep Cu from the longest polygranular segment, and significantly increases the time to failure. In the optimal case the transgranular‐slit failure mechanism is suppressed, and the bamboo grain fails by diffuse thinning to rupture. Preaging is particularly effective in increasing the lifetimes of lines that contain very long polygranular segments, and has the consequence that the time to first failure in an array of lines is much longer than predicted by a log‐normal fit to the distribution of failure times.

Fatigue crack propagation in high-strength A286 steel was studied by comparing crack growth rates determined from: (1) conventional long-crack propagation tests, (2) closure-free long-crack tests at constant Kmax, and (3) small-crack propagation tests. Small-crack growth rates were measured by following the growth of surface cracks in samples cycled from near-zero stress to 0.5 or 0.8σy. While most of the surface cracks became dormant shortly after nucleation, some grew into long cracks, and some of these propagated at cyclic stress intensities below the long-crack threshold, ΔKth (or ΔK th eff , the threshold cyclic stress intensity after crack closure effects have been removed). Surface cracks grew more rapidly than long cracks at the same ΔKor ΔKeff. The small-crack effect disappeared when the crack-tip plastic zone size became greater than the grain size. The results show that the absence of crack closure is only one of several factors that influence short-crack growth in A286 steel. Both peak stress and microstructural effects are important. Microstructural effects are apparently responsible for subthreshold crack growth; the cracks that grow at ΔK < ΔK th eff form and grow in statistically weak regions of the microstructure.

We report the development of a method for quantitative, in situ nanoindentation in an electron microscope and its application to study the onset of deformation during the nanoindentation of aluminum films. The load-displacement curve developed during in situ nanoindentation shows the characteristic ''staircase'' instability at the onset of plastic deformation. The instability corresponds to the first appearance of dislocations in previously defect-free grains, and occurs at a force near that measured in conventional nanoindentation experiments on similarly oriented Al grains. Plastic deformation proceeds through the formation and propagation of prismatic loops punched into the material, and half-loops that emanate from the sample surface. This new experimental technique permits the direct observation of the microstructural mechanisms that operate at the onset of deformation.

The structure of dislocation cores in elastically anisotropic materials is considered. A definition of the dislocation core radius is introduced and used to demonstrate that the elastic anisotropy that develops near a composition driven phase transition, such as that predicted for the Ti-Nb based alloys known as gum metals, can drive dislocation core radii to infinity. Under these circumstances, dislocation cores necessarily overlap. The atomic scale structures predicted to arise from core overlap in Ti-V alloys are reminiscent of nanodisturbances observed in gum metals.

The microstructure that results from a martensitic transformation is largely determined by the elastic strain that develops as martensite particles grow and interact. To study the development of microstructure, it is useful to have computer simulation models that mimic the process. One such model is a finite-element model in which the transforming body is divided into elementary cells that transform when it is energetically favorable to do so. Using the linear elastic theory, the elastic energy of an arbitrary distribution of transformed cells can be calculated, and the elastic strain field can be monitored as the transformation proceeds. In the present article, a model of this type is developed and evaluated by testing its ability to generate the preferred configurations of isolated martensite particles, which can be predicted analytically from the linear elastic theory. Both two- and three-dimensional versions of the model are used. The computer model is in good agreement with analytic theory when the latter predicts single-variant martensite particles. The three-dimensional model also generates twinned martensite in reason- able agreement with the analytic predictions when the fractions of the two variants in the particle are near 0.5. It is less successful in reproducing twinned martensites when one variant is dom- inant; however, in this case, it does produce unusual morphologies, such as “butterfly mar- tensite,” that have been observed experimentally. Neither the analytic theory nor the computer simulation predicts twinned martensites in the two-dimensional transformations considered here, revealing an inherent limitation of studies that are restricted to two dimensions.

This paper considers the evolution of equilibrium shape during the coarsening of a system of cubic precipitates in a cubic matrix with positive anisotropy [Delta] = C[sub 11] - C[sub 12] - 2C[sub 44] [gt] 0). The system is assumed to have homogeneous elastic constants and isotropic surface tension. The low-energy shapes include the sphere, and the octahedron, tetrahedron and plate with [l brace]111[r brace] faces. Minimization of the sum of the elastic and surface energies shows that the sphere is preferred at arbitrarily small sizes, but ordinarily transforms into a tetrahedron, and finally in a plate as size increases. When [Delta] [gt] 0.79C[sub 11] the octahedron is preferred for a small range of sizes between sphere and tetrahedron. Analytic expressions are given from the equilibrium shape transitions. The results are compared to experimental observations of shape changes during coarsening in (mg, Y)-ZrO[sub 2]. The experimentally observed absence of octahedral shaped precipitates and the size at which tetrahedral shaped precipitates become stable in this system are consistent with the theoretical predictions.

This paper reports a study of the effect of Cu precipitation on electromigration failure in Al‐2Cu‐1Si thin‐film conducting lines. The films were 0.5 μm in thickness, and patterned to widths of 1.3 and 4 μm, providing width‐to‐grain‐size ratios (W/G) of approximately 0.5 and 2. The lines were aged for various times at 226 °C, and were then tested to failure at a current density of 2.5×106 A/cm2. Scanning and transmission electron microscopy were used to study the Cu precipitate distribution, its evolution during aging and electromigration, and the microstructural failure mechanism. Aging produces a dense distribution of intragranular θ’ (Al2Cu; coherent), with stable θ (Al2Cu; incoherent) in the grain boundaries. The θ’ is replaced by θ as aging proceeds. In the wide lines (W/G≊2), the mean time to failure (MTF) increases slowly and monotonically with prior aging time. The failure happens through the growth and coalescence of intergranular voids. In the narrow lines (W/G≊0.5), both the MTF and the time to...