Misfit Stress Research Articles

Effects of intergranular hydride precipitation on the mechanical behavior of bicrystalline zirconium: A molecular dynamics-based study

This article investigated the impact of intergranular hydride precipitation on the mechanical behavior of zirconium (Zr) bi-crystals using molecular dynamics (MD)-based simulations. Uniaxial tensile tests were conducted to explore the effects of hydride precipitation on symmetric and asymmetrical tilt grain boundaries (GBs) of Zr with [0 1‾ 10] as the tilt axis. The stress-strain curves and deformation governing mechanism of bi-crystalline Zr were analyzed using the MD-based simulations in conjunction with the COMB force field. Misfit stress and tensile stress degradation induced by hydride precipitation were evaluated to understand their correlation with GB misorientation angles. Hydride precipitation induced the residual stresses in the vicinity of GB plane and mitigates the overall mechanical properties. It was predicted from the simulations that GBs with low misfit stress develop a lower mismatch between the lattice of Zr and hydride precipitate. Consequently, the effect of hydride on the tensile strength gets nullify. In contrast, the effects of hydrides are more pronounced on the tensile strength of Zr containing low-energy GBs in conjunction with high-misfit stress. The study further reveals that intergranular hydride precipitation causes the hydride embrittlement effect in Zr bicrystals, which intensifies with large size hydride precipitate. These findings contribute to an atomistic-level understanding of intergranular hydride-induced embrittlement and its correlation with Zr grain boundary orientation.

Unraveling the mechanics of directional coarsening in single crystal Ni-based superalloys via laser peening: Insights from experimental characterization and microstructural analysis

Surface treatment techniques, like laser peening, enhance the longevity of Ni-based superalloy components by reinforcing their microstructure against surface-initiated damage. Recent findings suggest that these methods may also influence precipitate coarsening behavior at high temperatures, leading to rafting phenomena. This study extensively examined γ’ rafting in single crystal Ni-based superalloy CMSX-4 post laser peening and heat treatment. X-ray diffraction revealed surface compressive stresses (-400 MPa to -800 MPa), transitioning to tensile stresses at greater depths before returning to an unstressed state. Correlation with electron microscopy indicated horizontal coarsening in compressive regions and vertical coarsening in tensile regions due to misfit and residual stresses aiding diffusion. Plastic strain near the LPed surface was measurably increased with lattice misorientation values around 5° before returning to an unstrained state after heat treatment due to rafting-aided recovery and defect reorganization. Secondary γ’ precipitates with a radius of approximately 10 nm occupied γ channels between rafted precipitates, indicating solute element diffusion and supersaturation. Energy dispersive x-ray spectroscopy showed a significant depletion of γ’-forming elements around rafted primary precipitates, highlighting preferential solute diffusion.

Morphological stability of electrostrictive thin films

A large electric field is typically present in anodic or passive oxide films. Stresses induced by such a large electric field are critical in understanding the breakdown mechanism of thin oxide films and improving their corrosion resistance. In this work, we consider electromechanical coupling through the electrostrictive effect. A continuum model incorporating lattice misfit and electric field-induced stresses is developed. We perform a linear stability analysis of the full coupled model and show that, for typical oxides, neglecting electrostriction underestimates the film’s instability, especially in systems with a large electric field. Moreover, a region where electrostriction can potentially provide a stabilizing effect is identified, allowing electrostriction to enhance corrosion resistance. We identified an equilibrium electric field intrinsic to the system and the corresponding equilibrium film thickness. The film’s stability is very sensitive to the electric field: a 40 percent deviation from the equilibrium electric field can change the maximum growth rate by nearly an order of magnitude. Moreover, our model reduces to classical morphological instability models in the limit of misfit-only, electrostatic-only, and no-electrostriction cases. Finally, the effect of various parameters on the film’s stability is studied.

Thermal Misfit and Diffusion Induced Stresses of Cu-Al Intermetallics in Microelectronics Wire Bonding

The thermosonic bonding technique is a widely used method for Cu wire interconnections. However, issues arise due to volumetric changes in intermetallic compounds (IMCs) formed at the Cu-Al bonding interface, leading to voids in the Cu-Al IMC layer. This problem is exacerbated after annealing, such as in high-temperature Storage (HTS). In this study, a statistical modelling approach was employed to quantitatively analyse stress, studying the evolution and characteristics of the interfacial microstructure in the thermosonic Cu wire-Al bond pad system. Microstructural analysis focused on Cu-Al IMC crystallography and compositional classification. A stress model was proposed, considering both thermal misfit and diffusion-induced stresses. Results showed that interfacial stress generally increased with higher bonding temperatures. The influence of forming gas supply was relatively minor, with oxide layers minimally impeding Cu-Al interdiffusion during Cu-Al IMC formation. This stress modelling technique hold potential as a valuable failure analysis tool for implementing Cu wire in various industries.

On the role of plastic relaxation in stress assisted grain boundary oxidation

The influence of plasticity on the high-temperature stress-assisted grain boundary oxidation of nickel-based superalloys used in applications such as turbine rotor discs is investigated using the method of discrete dislocation plasticity (DDP). The misfit stress fields of nib-shaped intrusions are captured by a continuous distribution of edge dislocations whose extra half planes represent the volumetric misfit of the oxide, which is implemented in a planar formulation of DDP by invoking the linear superposition principle. DDP simulations show that stresses generated by an intrusion several microns or more in size are large enough to generate dislocation pileups with associated stresses at the intrusion interface on the order of 1 GPa, which in turn lead to localized growth and morphology change of the intrusion by stress-assisted diffusion. This morphology change relaxes the compression stress inside the intrusion near the base, and therefore increases the fracture resistances of the intrusion. The effects of applied loading and background plasticity on the growth rate of the intrusion in defect-free and prestrained samples are predicted. It is found that applied tensile stress generally increases grain boundary oxidation, while in prestrained samples the enhancement of the intrusion growth rate by the applied load is insignificant due to dislocation pile-ups ahead of the oxidation process.

Misfit and the mechanism of high temperature and low stress creep of Ni-base single crystal superalloys

The present work proposes a new elementary deformation mechanism which governs high temperature and low stress creep of single crystal superalloys (SXs), where the misfit between the γ- and the γ′-phase plays a central role. In the coherent two phase SX microstructure, there is a tendency to minimize the overall elastic strain energy. This is accomplished by the formation of dislocation networks in the γ-phase close to the γ/γ’-interfaces. The stress fields of the network dislocations and misfit stresses accommodate each other to keep the overall strain energy of the system at a minimum. Previous work has shown that dynamic recovery is associated with knitting-out reactions, where dislocations from the network shear the γ’-phase and annihilate with dislocations of opposite sign on the other side of the γ’-phase region. Due to the presence of the misfit this results in an increase of elastic strain energy which is counteracted by coupled knitting-in reactions where newly arriving γ-channel dislocations re-establish the minimum energy configuration. Here we provide microstructural evidence for knitting-out and knitting-in reactions and show that while these reactions clearly occur, dislocation network spacings stay constant. The misfit between the γ- and the γ′-phase accounts for a constant network spacing. Dislocation networks are not static but represent dynamic steady state equilibrium structures in an evolving microstructure. Knitting regular networks requires climb processes which are suggested to be rate controlling. This new view of high temperature and low stress creep mechanism of SXs allows to rationalize previous results published in the literature.

Significant dislocation strengthening of stainless steel 316L via co-directed energy deposition of silica

This study aims at fully utilizing dislocation strengthening for higher hardness of stainless steel 316 L through two methods: 1) Multi-layer directed energy deposition (DED) is utilized to intensify dislocation generation induced by thermal cycling compared to single-layer DED. 2) Ultra-low thermal expansion coefficient silica particles are incorporated into a 316 L substrate, utilizing thermal misfit stresses between particles and the matrix. Silica particles, dispersed within the substrate, enable both multi-layer DED and surface DED. Nine samples (labeled as 1 L–9 L, respectively) with varying deposition layers from 1 to 9 are prepared. As deposition layers increase, silica particles agglomerate and elongate, promoting micro-crack formation in the matrix. Increasing deposition layers is found to alter gradually the solidification structure from planar to cellular and columnar dendrites, and transform the primary austenite to martensite (approximately 100 % at 9 L). This phase transformation is driven by oxygen-affine Cr and Mn elements diffusing into silica particles. Surprisingly, the hardness is significantly increased from about 170 HV at the base metal, 180–220 HV at 1 L–5 L, and 270 HV at 6 L, to maximum 300–330 HV at 8 L. This improvement is theoretically explained by significant dislocation strengthening mechanism (Δρ ∼ 6.70 × 1014 m−2) amplified by the multi-layer silica DED process. Furthermore, distinct dislocation structures including dislocation entanglement around silica particles, patterned dislocation walls, and nano-lamellae pile-ups of dislocations are found at 8 L from transmission electron microscope analysis. The strengthening origins and the potential of SiO2/316 L bulk composites are briefly explored.

Misfit stress and energy in composite nanowire with polygonal core

In this article we present for the first time an analytical solution to the boundary-value problem in the classical theory of elasticity for a core-shell cylinder with an eccentric prismatic core having a trapezoidal cross section and subjected to uniform dilatation eigenstrain. In doing so, we represent the trapezoidal prism as a superposition of long straight dilatational lines located along the cylinder axis. The complex potential approach has been employed to satisfy the boundary conditions on the cylinder free surface. Found in a concise and transparent closed form, the elastic stresses exerted by the dilatational line and dilatational prismatic inclusion (of trapezoidal cross section) in cylindrical body are demonstrated with maps. The mean stress is employed to obtain the analytical expression of strain energy stored by the dilatational inclusion in form of regular prism symmetrically placed in cylindrical body. It is proved that the strain energy is identical to the one of cylindrical inclusion with the same cross section area.

Analysis of implant-supported cantilever fixed partial denture: An in vitro comparative study on vertical misfit, stress distribution, and cantilever fracture strength.

To evaluate the vertical misfit, stress distribution around dental implants, and cantilever fracture strength of 3-unit implant-supported cantilever fixed partial dentures (FPDs) using frameworks made from different materials and manufacturing techniques. Forty FPDs were fabricated and divided into 5 groups (n = 8) based on the framework material used: LAS Co-Cr (Conventional casting-laser welding); TIG Co-Cr (Conventional casting -TIG welding); OP Co-Cr (Conventional casting-one-piece); CAD Co-Cr (CAD-CAM); and CAD Zr (CAD-CAM ZrO2). The vertical misfit was evaluated before porcelain application (T1) and before (T2), and after thermomechanical cycling (T3) by stereomicroscopy. Cantilever fracture strength was tested with a 50 kN (5000 kgf) load cell at a crosshead speed of 0.5mm/min. Qualitative and quantitative photoelastic analysis was performed to evaluate stress distribution at seven specific points in five FPDs (n = 1/group) subjected to occlusal loading. Only the molar showed interaction among the three factors (G × S × T; F(20.932) = 1.630; p = 0.044). Thermomechanical cycling (T2 vs. T3) had a significant effect on intra-group vertical misfit in molar, especially in LAS Co-Cr (Δ = 5.87; p = 0.018) and OP Co-Cr (Δ = 5.39; p = 0.007), with no significant effect in premolar (p > 0.05). Ceramic application combined with thermomechanical cycling (T1 vs. T3) caused a significant intra-group increase in vertical misfit in all groups, both in the molar and premolar (p < 0.05). OP Co-Cr was associated with greater vertical misfit and stress concentration. Frameworks manufactured by the CAD-CAM system exhibited lower vertical misfit and better stress distribution. FPDs with metal frameworks (>410.83 ± 72.26 N) showed significantly higher fracture strength (p < 0.05) than zirconia (277.47 ± 39.10 N), and the first signs of ceramic veneering fracture were observed around 900 N. FPDs with frameworks manufactured using a CAD-CAM system appear to be associated with lower vertical misfit and better stress distribution, although the section of the frameworks followed by welding may be a viable alternative. In addition, metal frameworks exhibit high fracture strength.

Dislocation in a Strained Layer Embedded in a Semi-Infinite Matrix

Abstract The misfit stress in a thin layer embedded in a semi-infinite matrix has been first determined near the free surface of the structure, using the virtual dislocation formalism. From a Peach–Koehler force analysis, the different equilibrium positions (unstable and stable) of an edge dislocation gliding in a plane of the layer inclined with respect to the upper interface and emerging at the point of intersection of the upper interface and this free surface have been then characterized with respect to the lattice mismatch and the inclination angle of the gliding plane. It has been found that the dislocation may exhibit stable equilibrium position near the interface and/or near the free surface. A diagram of the position stability has been then determined versus the misfit parameter and the inclination angle. The energy variation due to the introduction of an edge dislocation from the free surface until the matrix layer interface has been finally determined, when the dislocation is gliding in the plane inclined with respect to the interface horizontal axis. A critical thickness of the layer beyond which the formation of the dislocation in the interfaces is energetically favorable has been finally determined as well as its position with respect to the free surface in the lower interface.

Evolution of phase interface microstructure and its effects on stress rupture property of a 4th generation nickel-based single crystal superalloy after thermal exposure

Lattice constants, phase interface microstructure and stress rupture properties of nickel-based single crystal superalloy after thermally exposed at 1100 °C for different time were investigated using synchrotron radiation diffraction and transmission electron microscopy techniques. The results show that the lattice constants of γ and γ' phase at room temperature decrease and the misfit at room temperature becomes more negative after 200 h exposure, and these parameters remain unchanged after exposure for 500 h. The release of misfit stress during thermal exposure is completed by the transformation from coherent γ/γ' interface to semi-coherent interface as well as the formation of misfit dislocation. The misfit dislocation network generated during thermal exposure is mainly rectangular shape, and its formation process is analyzed in detail. Additionally, it is found that the stress rupture lives decrease obviously after thermal exposure, while the morphology and size of interfacial dislocation network of thermally exposed alloys after rupture are very similar with that of unexposed alloy. The relation of γ' phase morphology and interfacial dislocation network to the stress rupture property deterioration has been discussed.

Thermomechanical model of an oxide-confined GaAs-based VCSEL emitter

A thermomechanical model for an oxide-confined GaAs-based VCSEL emitter is presented. The impact of the lattice mismatch, the oxide shrinkage and the thermal stress on the mechanical reliability is evaluated. Under standard operating conditions, calculations show that the temperature increase has a negligible influence on the overall mechanical stress. The oxide shrinkage highly deforms the epitaxial structure at the edge of the optical aperture. At oxide corners, the calculated stress is beyond the experimental yield strength of GaAs micro-pillars, enabling the nucleation of the dislocations forming dark line defects. The high misfit stress in the quantum well layers can favor there the dislocation propagation.

Effect of Mo on microstructural stability of a 4th generation Ni-based single crystal superalloy

The microstructural stability during thermal exposure at 900 °C of Ni-based single crystal superalloys with various Mo content was investigated. The coarsening of γ′ precipitates and formation of TCP (topologically close-packed) phases were discussed in detail. The LSW theory and TIDC theory were applied to study the coarsening behavior of γ′ particles, and both models fitted well with the experimental results. Increasing Mo content enhanced the partitioning behavior of alloying elements, thus increasing the lattice misfit and interfacial stress of γ′/γ phases. Additionally, Mo addition also decreased γ′ coarsening rate by retarding the diffusion process of elements. However, Mo addition significantly promoted the precipitation of TCP phases, consuming massive solution strengthener elements, such as Re, W and Mo. TCP precipitation may significantly limit the creep life at 900 °C.

Dislocation equilibrium positions in bilayer structures

The stability of an edge dislocation embedded in a two-dimensional structure composed of one layer of ZnS and one layer of Ge has been theoretically investigated from a Peach–Koëhler force-based analysis in the absence of misfit stress and layer bowing effects. The effect of thickness ratio between the two layers of heterogeneous elastic coefficients has been characterized on the different equilibrium positions of the dislocation through the study of the climbing component of the Peach–Koëhler force. It is found that the number (from 3 to 5) and nature (stable or unstable) of these equilibrium positions distributed in both layers vary significantly as a function of the thickness ratio.

CALPHAD informed design of multicomponent CoNiCr-based superalloys exhibiting large lattice misfit and high yield stress

Usually, Co-based superalloys contain a high fraction of W and/or Mo. The refractory elements stabilize the precipitate phase, but cause a high density. In this work, new L12-phase hardened, low-density CoNiCr-based superalloys were developed with the assistance of CALPHAD calculations. Several alloys were studied experimentally and their microstructures, elemental distributions, lattice parameters and the lattice misfit between the γ and γ′ phases were evaluated using scanning electron microscopy, transmission electron microscopy, atom probe tomography and high energy X-ray diffraction. The alloys exhibit a very high misfit, good phase stability and excellent mechanical strength. It was found by hardness tests that a two-step heat treatment improves the strength of the new alloys even further. In comparison with conventional Co-based superalloys, Co–Al–W based superalloys and Co–Ti based superalloys, as well as Ni-based superalloys, i.e. Udimet 720Li, they have a low mass density and high yield stress. They also overcome the problem of a generally low lattice misfit of previous L12-phase hardened CoNiCr-based superalloys with high Ni and Cr contents. As a result, they show cuboidal-shaped precipitates similar to Co–Al–W and Co–Al–Mo based superalloys.

Nanotomographic observation and statistical analysis of overcharging induced cracks in LiCoO2 single crystalline particles

Particle fracture represents an important mode of battery electrode degradation. Extensive cracking occurs in the layered oxide cathodes of lithium-ion rechargeable batteries when they are charged beyond safe operational voltages. In this paper, we analyze the morphology and distribution of cracks in over 100 overcharged LiCoO2 (LCO) single-crystalline particles imaged via X-ray nanotomography. We observe a strong particle size dependence in both nucleation and growth of cracks, with percentage of cracked particles, crack size, and crack surface area per unit volume all increasing significantly with particle volume. Increasing the cutoff voltage above 4.6V is found to trigger much more pronounced crack growth, which we attribute to the large misfit stress caused by the H1-3 to O1 phase transition. This study offers valuable statistical insights into the fracture behavior of layered oxide cathodes and reveals the importance of particle size control on electromechanical degradation of battery electrodes.

Misfit strain induced out-of-interface prismatic dislocation loops in axially inhomogeneous hybrid nanowires

The possibility of forming the misfit-strain-induced out-of-interface prismatic dislocation loops (PDLs) in axially inhomogeneous hybrid two-phase nanowires with a transverse interface is theoretically studied. It is shown that, due to the misfit stresses caused by the contact of two crystalline materials with different lattice parameters, the PDLs of certain radii can generate at certain distances from the interface when the nanowire radius is larger than a critical value, which depends on the lattice misfit. The critical parameters of the relaxation process are calculated and discussed in detail.

Prismatic dislocation loops in crystalline materials with empty and coated channels

This paper presents for the first time an analytical solution to the boundary-value problem in the theory of elasticity for a circular prismatic dislocation loop (PDL) coaxial to a hollow cylindrical channel in an elastically isotropic infinite matrix. The stress fields and energy of the PDL are calculated and analyzed in detail. Based on the solution, a theoretical model for the misfit stress relaxation through the formation of a misfit PDL around a misfitting nanotube embedded in an infinite matrix is suggested. The critical radii of the embedded nanotube are found and discussed. It is shown that, for thin nanotubes prepared by nanolayer growth on the initial channel surface, there are two critical inner radii of the nanotube, between which the formation of a misfit PDL is energetically favorable.

Misfit stress relaxation in wide bandgap semiconductor heterostructures with trigonal and hexagonal crystal structure

In this work, we consider film/substrate semiconductor heterostructures with a hexagonal (wurtzite) and trigonal (corundum) crystal structure. We show that the differences between the stress level in the α-Ga2O3/α-Al2O3 heterostructure with the corundum crystal structure and the stress level in the GaN/AlN heterostructure with the wurtzite crystal structure do not exceed 50%. We study the effect of Al composition x and growth direction of the heterostructure on the critical film thickness for misfit dislocation formation in α-(AlxGa1−x)2O3/α-Al2O3 heterostructures. We provide a comparison between theoretical calculations of the critical film thickness and experimental data on the film thickness, at which the misfit dislocations were observed in α-(AlxGa1−x)2O3/α-Al2O3 heterostructures.

Misfit Stress in Radial Core-Shell Nanowires with Diffuse Interface Boundaries

The elastic models of radial core-shell nanowires with diffuse interphase boundaries are suggested. The concept of eigenstrain is employed to consider a misfit stress distribution induced by diffusive interfaces with different range of distinctness. The eigenstrain profile described by the misfit parameter is approximated by piecewise-linear, error and arctangent functions. For these approximations the elastic stresses in core-shell nanowires are analytically derived, illustrated with plots and discussed in detail.