High Misfit Strain Research Articles

An experimental and statistical study on the characteristics of non-metallic inclusions that serve as hydrogen-induced crack nucleation sites in pipeline steel

This study consists of a statistical study to identify spatial distribution parameters of non-metallic inclusions (NMIs) at hydrogen-induced cracking (HIC) nucleation sites in both low-strength and high-strength steel pipes. The electrochemical cathodic charging method was used to induce HIC in pipeline steel plates, and the nucleation of the HIC was monitored using straight beam ultrasonic testing. Optical microscopy (OM) and scanning electron microscopy (SEM) were used to evaluate the shape, size, area fraction, and separation distance of NMIs. The hydrogen microprint technique (HMT), electron backscattered diffraction (EBSD) analysis, and finite element (FE) stress analysis were performed to characterize HIC nucleation sites. The findings showed that cubical and spinal NMIs, characterized by strong hydrogen trapping capacity due to high misfit strain and von Mises stress, are favored sites for HIC nucleation. The main finding of this study is that the shape and sharpness of NMIs are the factors that determine when NMIs will be a HIC nucleation site, rather than size, as generally accepted.

Novel machine learning-based prediction approach for nanoindentation load-deformation in a thin film: Applications to electronic industries

Electronics industries, notably device fabrication industries, deposit thin films on thick substrates to create various devices such as sensors, actuators, LED Multi-Quantum Well (MQW), and High Electron Mobility Transistors (HEMT). The lattice and thermal expansion coefficient mismatch between the thin film and the substrates causes misfit strain generation. The misfit strain can not only cause defect formation but can also change the local deformation pattern. The altered deformation pattern can have an impact on electronic device performance. Therefore, the load-deformation behaviour of thin films deposited on a thick substrate has been investigated using the nanoindentation modelling approach. Two alternative modelling strategies have been employed.The finite element analysis-based nanoindentation simulation was carried out to evaluate the load required for a fixed deformation in the thin film with changing misfit strain between the thin film and the substrate. The next stage was further predicting the load required for indentation deformation in the thin film at higher misfit strain using a machine learning-based linear regression model. Gallium nitride thin filmlayer on silicon and sapphire substrate were considered as case studies for this purpose. It was discovered that as the misfit strain between the substrate and the thin film increases, so does the thin film's elastic recovery and brittleness. Both the FEM and the machine learning model results were validated against published experimental findings available in the literature. The machine learning model presented in this work can be utilized to evaluate the performance of devices like MEMS, NEMS, LEDs, etc. without carrying out iterative nanoindentation experiments or FE simulations, which will aid in reducing the overall cost of these optoelectronic devices and increase the overall profit of the electronic industries.

Size Reducing Rupture during “Growth” of LnF3 (Ln = La, Lu, Y) Nanocrystals Due to Cogeneration of Structure and Stress

Crystal growth involves an increase in the average size of crystals even during Ostwald ripening, wherein larger crystals grow at the expense of smaller crystals. In contrast, we observed particle size reduction due to rupture during the growth of polycrystalline LnF3 (Ln = Lu, Y, La) nanoparticles. We rationalize this by the feature of the growing crystal to evolve toward the most stable native crystal form via several metastable intermediate non-native amorphous or crystalline structures with a significant change in density, resulting in high misfit strain and generation of stress within the single nanoparticle. The stress promotes the propagation of already existing flaws in the crystal, leading to the rupture of nanocrystals and a subsequent decrease in crystallite size. Results from finite element elastic simulations also support the propagation of flaws leading to nanocrystal rupture if the fracture toughness of the materials is low. The ligand plays an essential role in the observation of this phase of crystal growth by retarding the growth kinetics.

A phase-field study of elastic stress effects on phase separation in ternary alloys

Most of the commercially important alloys are multicomponent, producing multiphase microstructures as a result of processing. When the coexisting phases are elastically coherent, the elastic interactions between these phases play a major role in the development of microstructures. In order to elucidate the key effects of elastic stresses on microstructural evolution when more than two misfitting phases are present in the microstructure, we have developed a microelastic phase-field model in two dimensions to investigate microstructural evolution during phase separation in a ternary alloy system with coherent elastic misfit. Numerical solutions of a set of coupled Cahn-Hilliard equations for the composition fields govern the spatiotemporal evolution of the three-phase microstructure. The model includes elastic driving forces arising due to coherency strain interactions between the phases. We systematically vary the misfit strains (magnitude and sign) between the phases along with the bulk alloy composition to study their effects on the morphological development of the phases and the resulting phase separation kinetics. We also vary the ratio of interfacial energies between the phases to understand the interplay between elastic and interfacial energies on morphological evolution. The sign and degree of misfit affect strain partitioning between the phases during spinodal decomposition, thereby affecting their compositional history and morphology. Moreover, strain partitioning affects solute partitioning and alters the kinetics of coarsening of the phases. The phases associated with higher misfit strain appear coarser and exhibit wider size distribution compared to those having lower misfit. When the interfacial energies satisfy complete wetting condition, phase separation leads to development of stable core-shell morphology depending on the misfit between the core (wetted) and the shell (wetting) phases.

Oxidation behavior of dense SiOC monolithics: The oxide scale development

Forming stable and continuous oxide scale is the key to resist oxidation by acting as a surface-diffusion barrier to reduce further oxygen attack. Oxidation behavior of dense SiOC monolithics was studied from 900 °C to 1200 °C for up to 18 h. The oxide scale formed at 1000 °C and 1200 °C was ∼106 μm and ∼81 μm in thickness, respectively. High thermal misfit strain induced by the large thickness and volume shrinkage originated from crystallization of silica resulted in the scale cracking with oxidation time. However, the scale formed at 1100 °C remained dense and thin (∼43 μm) without any visible defects, protecting the SiOC base effectively.

Diffusive molecular dynamics simulations of lithiation of silicon nanopillars

We report diffusive molecular dynamics simulations concerned with the lithiation of Si nano-pillars, i.e., nano-sized Si rods held at both ends by rigid supports. The duration of the lithiation process is of the order of milliseconds, well outside the range of molecular dynamics but readily accessible to diffusive molecular dynamics. The simulations predict an alloy Li15Si4 at the fully lithiated phase, exceedingly large and transient volume increments up to 300% due to the weakening of SiSi iterations, a crystalline-to-amorphous-to-lithiation phase transition governed by interface kinetics, high misfit strains and residual stresses resulting in surface cracks and severe structural degradation in the form of extensive porosity, among other effects.

High-quality TiN/AlN thin film heterostructures on c-sapphire

We have developed TiN/AlN/c-sapphire epitaxial heterostructures and compared it with TiN/c-sapphire epitaxial heterostructures, needed for GaN-based LEDs and lasers. AlN is used as a buffer layer to provide a high misfit strain and facilitate the 2D growth on sapphire. The large misfit strain between sapphire and AlN makes this substrate a great candidate for GaN-based devices because it guarantees a full relaxation of AlN thin films through domain matching epitaxy paradigm. TiN can also act as an excellent contact and bottom electrode for Ⅲ-Ⅴ nitrides. Also, the introduction of TiN as a buffer layer decreases the critical thickness beyond which dislocations can grow in GaN thin films due to higher misfit strain compared to sapphire, which also improves the quality of potential GaN thin films. The selected-area-electron-diffraction patterns, scanning transmission electron microscopy, and transmission Kikuchi diffractions along with atomic arrangement simulations revealed that films are epitaxial with the following relationships: TiN<101>‖AlN[1¯21¯0]‖sapphire[011¯0] (in-plane), and TiN<111>‖AlN[0001]‖sapphire[0001] (out-of-plane). This is equivalent to a 30° rotation of Al basal plane in AlN with respect to that in sapphire. In TiN/c-sapphire epitaxial platforms, there is a 30° rotation: TiN<101>‖sapphire[011¯0] (in-plane), and TiN<111>‖sapphire[0001] (out-of-plane). It is shown that these heterostructures are fully relaxed in terms of misfit strains and only thermal strain stays as unrelaxed. The domain matching epitaxy paradigm is used to rationalize the epitaxial growth. The details of dislocations nucleation and glide in these heterostructures were studied and the results also discussed to elucidate the mechanism of strain relaxation.

Development of Grain Boundary Precipitate-Free Zones in a Ni-Mo-Cr-W Alloy

In this study, the morphology and development of precipitate-free zones (PFZs) near grain boundaries (GBs) in low coefficient of thermal expansion (CTE) Ni-Mo-Cr-W alloys (based on Haynes 244) have been investigated as a function of thermal history and composition using electron microscopy techniques. It is shown that the formation of wide, continuous PFZs adjacent to GBs can be largely attributed to a vacancy depletion mechanism. It is proposed that variations in the vacancy distributions that develop after solution heat treatment (SHT) and subsequent quenching and aging greatly influence the development of the γ′-Ni2(Mo,Cr) precipitates during the aging process and result in the development of PFZs of varying sizes. The relatively large (5 to 10 μm) PFZs are distinct from the smaller, more common PFZs that result from solute depletion due to GB precipitation that are typically observed after prolonged aging. During the course of this investigation, heat treatment parameters, such as aging time, SHT temperature, cooling rate after SHT, and heating rate to the aging temperature—all of which change vacancy concentration and distribution adjacent to GBs—were investigated and observed to have significant influence on both the size and morphology of the observed PFZs. In contrast to results from other Ni-based alloys studied previously, PFZ development in the current alloys was observed across a broad range of aging temperatures. This appears to be due to the high misfit strain energy of the γ′ precipitates, resulting in a nucleation process that is sensitive to vacancy concentration. It is also shown that a slightly modified alloy with higher Mo concentrations develops smaller, more typical PFZs; this is presumably due to an increased driving force for γ′ precipitation which overshadows the influence of misfit strain energy, thereby decreasing the sensitivity of precipitation on vacancy concentration.

Precipitation in a copper matrix modeled byab initiocalculations and atomistic kinetic Monte Carlo simulations

A kinetic Monte Carlo approach is used to study the influence of Cr, Fe, Al, or Mg addition on the precipitation in a Cu–Ni–Si alloy. The simulation method is based on a vacancy diffusion model. The crucial parameters of this method are the pairwise mixing energies of all contained elements which are determined by ab initio calculations. The number of dissolved atoms in equilibrium state is used to estimate the influence of Cr, Fe, Al, or Mg on the electrical conductivity. In order to estimate the influence of the alloying elements on strength ab initio calculations of misfit strain at the Cu/Ni3Si interface are performed. The atomistic kinetic Monte Carlo (AKMC) simulations reveal that Cr, Fe, Al, and Mg atoms are located at different positions: Mg and Al atoms are preferably located at the interface of Ni–Si precipitates and Cu matrix, Cr atoms diffuse into Ni–Si precipitates, and Fe atoms form Fe clusters surrounded by Ni–Si shells. Cr addition leads to a significantly reduced fraction of atoms dissolved in the matrix which indicates an increase of electrical conductivity, whereas Mg addition results in a high misfit strain at the Cu/Ni3Si interface which can contribute to increased strength.

Study of strain effect on in-plane polarization in epitaxial BiFeO3thin films using planar electrodes

Epitaxial strain plays an important role in determining physical properties of perovskite ferroelectric oxide thin films because of the inherent coupling between the strain and the polarization. However, it is very challenging to directly measure properties such as polarization in ultrathin strained films, using traditional sandwich capacitor devices, because of high leakage current. Hence, a planar electrode device with different crystallographical orientations between electrodes, which is able to measure the polarization response with different electric field orientation, is used successfully in this work to directly measure the in-plane polarization--electric-field ($P$-$E$) hysteresis loops in fully strained thin films. We used BiFeO${}_{3}$ (BFO) as a model system and measured in-plane $P$-$E$ loops not only in the rhombohedral-like (R-like) BFO thin films but also in largely strained BFO films exhibiting the pure tetragonal-like (T-like) phase. The exact magnitude and direction of the spontaneous polarization vector of the T-like phase is deduced thanks to the collection of in-plane polarization components along different orientations. It is also shown that the polarization vector in the R-like phase of BiFeO${}_{3}$ is constrained to lie within the (1$\overline{\mathbf{1}}$0) plane and rotates from the [111] towards the [001] pseudocubic direction when the compressive strain is increased from zero. At high misfit strains such as $\ensuremath{-}4.4%$, the pure T-like phase is obtained and its polarization vector is constrained to lie in the (010) plane with a significantly large in-plane component, \ensuremath{\sim}44 \ensuremath{\mu}C/cm${}^{2}$. First-principles calculations are carried out in parallel, and provide a good agreement with the experimental results.

Thermal analysis of the ω nanophase transformation from the metastable β Ti–12Mo alloy

In this study, the thermal analysis of the ω nanophase transformation from a quenched metastable β Ti–12Mo alloy composition (mass%) was investigated by electrical resistivity and dilatometry measurements. The activation energy was observed to be 121 ± 20 kJ mol−1 (from resistivity measurements) and 114 ± 12 kJ mol−1 (from dilatometry measurements) during the early stage of the transformation process. The kinetic of the ω nanophase transformation was modelized by using the classical Johnson–Mehl–Avrami (JMA) theory and a modified Avrami (MA) analysis. An Avrami exponent close to 1.5 was found at the early stage of the transformation suggesting a pure growth mechanism from pre-existing nucleation sites. Nevertheless, it was observed a decrease of the Avrami exponent to 0.5 at higher transformed fraction demonstrating a dimension loss in the growth mechanism due to the existence of the high misfit strain at the interface β/ω.

Influence of depolarization field on polarization states in epitaxial ferroelectric thin films with nonequally biaxial misfit strains

Depolarization field and misfit strain are two important factors that greatly influence the properties of ferroelectric thin films. The present work studies the effect of depolarization field on polarization states in a single-domain ferroelectric thin film with nonequally biaxial in-plane misfit strains. Three coupled EulerLagrange equations are derived from the minimization of the total free energy and solved numerically. Misfitstrain–misfit-strain phase diagrams are constructed to represent the polarization states. Under the short-circuit boundary condition, the depolarization field shifts the phase boundaries in the phase diagrams, leading to the contraction and expansion of the regions of out-of-plane and in-plane phases, respectively. Under the opencircuit boundary condition, there exists an out-of-plane electretlike state under high compressive misfit strains when a surface polarization Pm is included.

Study on Microstructural Evolution and Age Hardening in High-Purity Al-Cu-Mg-Ag Alloy

By tensile test and transmission electron microscopy analysis, microstructural evolution and age hardening in an experimental high-purity Al-Cu-Mg-Ag alloy were investigated during a long period of ageing time. The results show that the experimental alloy has strong age-hardening response that the alloy strength rapidly increases to almost peak-aged condition after aged for only 2 hours. Ω phase and θ' phase control the hardening effects and grow independently as the ageing time prolonged. At the same time, fine secondary-precipitated θ' phase nucleates and grows near dislocations at fine laths of Ω phase which is resulted from the high misfit strain near Q/a interface. These new hardening precipitates compensate the strength loss due to the primary-precipitated Ω phase and θ' phase coarsening. Thus the alloy strength is only a little decrease after ageing for 50 hours at elevated temperature.

Influence of growth temperature and reactor pressure on microstructural and optical properties of InAlGaN quaternary epilayers

The effects of growth temperature and reactor pressure on the microstructural and optical properties of InAlGaN quaternary epilayers grown on thick GaN buffer by metalorganic chemical vapor deposition were investigated. The addition of Al atoms at the optimized growth temperature of an InGaN layer resulted in deep level emission and in pyramidal shaped surface pits due to island growth caused by the low mobility of the deposited Al atoms in spite of the reduction of in-plane misfit strain and full width at half maximum from high-resolution X-ray diffraction. As the growth temperature increased and reactor pressure decreased, the broad deep level emission and the density of surface pits were greatly reduced and the band-edge emission of InAlGaN epilayers was intense. Surface pits originating from the vertex of threading dislocations under high misfit strain were greatly affected by lowering the growth temperature while the band-edge emission strongly depended on reactor pressure. Therefore, we found that the reduced reactor pressure and the increased growth temperature enhanced lateral growth and were effective in growing the InAlGaN epilayers of optically and microstructurally good quality.

Growth and relaxation of (Zr,Y)O2 epitaxial layers analyzed by XRD reciprocal space mapping

Very thin polycrystalline and epitaxial yttria doped zirconia films have been realized using sol–gel processing. The lattice mismatch between the sapphire substrate and the zirconia crystals induces high misfit strain that we have determined using X-ray diffraction. Epitaxial films made of islands with sizes of several tens of nanometers are under very high stresses which are relaxed by the appearance of structural defects into the cubic zirconia crystals or by structural phase transition from the cubic to tetragonal zirconia form.

Geometrical Contribution to Yield Strength in Small Volumes

AbstractCritical thickness theory was developed to account for the ability of thin epitaxial metal and semiconductor layers to support high misfit or coherency strain. The thermodynamic equilibrium theory is correct, and is well approximated by a theory based on geometrical arguments. The latter theory is readily extended to arbitrary misfit strain profiles including linearly graded layers, for which a surface layer free of misfit dislocations. This result applies as well to linear strain gradients introduced by deformation, in which case the misfit dislocations are known as geometrically necessary dislocations. We show that a consequence of this surface layer is that the apparent yield strength of the material increases in small structures such as thin wires in torsion. Under large plastic deformation, even if the material is perfectly plastic, critical thickness theory also predicts an apparent work-hardening. The predictions of critical thickness theory are in excellent agreement with experimental data in the literature.

Mechanisms of misfit strain relaxation in epitaxially grown BLT (Bi4-xLaxTi3O12, x = 0.75) thin films

AbstractMechanisms of misfit strain relaxation in epitaxially grown Bi4-xLaxTi3O12 (BLT) thin films deposited on SrTiO3 (STO) and LaAlO3 (LAO) substrates have been investigated by means of transmission electron microscopy (TEM). The misfit strain of 20 nm thick BLT films grown on STO substrate was relaxed by forming misfit dislocations at the interface. However, cracks were observed in 100 nm thick BLT films grown on the same STO. It was confirmed that cracks were formed because of high misfit strain accumulated with increasing the thickness of BLT, that was not sufficiently relaxed by misfit dislocations. In the case of the BLT film grown on LAO substrate, the magnitude of lattice misfit between BLT and LAO was very small (~1/10) in comparison with the case of the BLT grown on STO. The relatively small misfit strain formed in layered structure of the BLT films on LAO, therefore, was easily relaxed by distorting the film, rather than forming misfit dislocations or cracks, resulting in misorientation regions in the BLT film.

Properties of InGaN/GaN Quantum Wells Grown by Metalorganic Chemical Vapor Deposition

ABSTRACTOptical and structural properties of InGaN/GaN quantum wells having growth interruption were investigated using high-resolution x-ray diffraction, photoluminescence and transmission microscopy. InxGa1−xN/GaN (x&gt;0.25) six pair quantum wells used in this study were grown on c- plane sapphire by metalorganic chemical vapor deposition. The growth interruption was carried out by closing the group-III metal organic sources before and after growth of InGaN quantum well layers. With increasing the interruption time, the quantum dot-like region and well thickness decreases due to indium re-evaporation or thermal etching effect. As a result, PL peak position is blue-shifted and intensity is reduced. The size and number of V-defect did not vary with interruption time. The interruption time is not directly related with formation of the defect. The V-defect in quantum wells originates at threading dislocations and inversion domain boundaries due to higher misfit strain.

Clustering and ordering of nitrogen in nuclear grade 316LN austenitic stainless steel

The high misfit strains associated with nitrogen addition and the high chemical affinity with chromium result in a significant driving force for the formation of Cr–N clusters in austenitic steels. The microstructural signatures of cluster formation in nuclear grade 316LN austenitic stainless steel during the early stages of aging at 1123 K are discussed. Aging beyond 25 h results in transformation of fcc clusters to hexagonal Cr 2N precipitates. Strain induced ordering of nitrogen in Cr 2N precipitates due to continued ageing is also highlighted.

Dislocations, twins, and cracks in In1–xGaxP/(001) GaAs heteroepitaxial layers

The occurrence of dislocations, twins, and cracks in In1–xGaxP (0.42 ≦ x ≦ 0.75), i.e. layers grown under compression and tension on (001) GaAs substrates of different misorientation (0°, 2°, 6°) towards [010], is studied for layers of various thicknesses (1 to 2.7 μm). On the surface of layers grown under tension corrugations due to preferred slip on (111) and (111) of the [110] zone can be observed. Additionally, fracture occurs at higher misfit strain, but in [110] direction, i.e. the cleavage plane is (110). The well-defined surface corrugations parallel to [110] correlate to twin lamellae located on inclined {111} slip planes. Twin growth proceeds by nucleation and propagation of 90° Shockley partial dislocations from a surface-near region towards the layer-substrate interface, leaving a less mobile 30° partial behind (in the case of tension). It seems that Maree's conception of spontaneous half loop nucleation at the free surface of a growing layer with critical thickness is favoured. In layers grown under compression the same model is used to explain the formation of dislocation networks. In this case the front segment of half loops generated at the free layer surface consists of a leading 30° Shockley partial and the 90° one trailing behind. Because of the lower mobility (higher friction force) of the first one, the twin formation is suppressed. From simple crystallographic arguments (InGaP belongs to the space group F 43m) it is concluded that in layers grown under tension partial dislocations with excess In/Ga atoms in their core can either be generated or be moved more easily than dislocations with excess P atoms. In layers grown under compression, on the contrary, partials with excess phosphorus in their core can be either generated or be moved more easily than partials with excess In/Ga atoms. Using the model of spontaneous half loop nucleation at the growing surface the demarcation line between the dislocation- and twin-free growth and that where defects occur is calculated and determined experimentally for deposition temperatures between 525 to 750°C. Moreover, the fracture toughness and precursor crack length for layers grown under tensional stress conditions are estimated using a modified Griffith equation and are KIC = 0.696 MPa m1/2 and lc = 216 nm (at 720 °C). Twin formation begins at 720 °C if a critical strain of ϵc = 3.1 × 10−3 and, therefore, a critical shear stress of τc = 87.5 MPa is exceeded.