Interfacial Misfit Dislocations Research Articles

Atomic study of fracture progress ofFe[110]/TMC[100] (TM=Ti,ZrandHf) semi-coherent interfaces

Using first-principle calculation in combination with the Chen–Möbius inversion method, we get the interfacial potentials of the Fe [110]/ TMC [100] ( TM = Ti , Zr and Hf ) interface system. Based on the interfacial potentials, we investigate the interfacial stability, misfit dislocations and tensile fracture of the semi-coherent interfaces of Fe [110]/ TMC [100] ( TM = Ti , Zr and Hf ). The different sizes of the misfit dislocation models are employed to compare the interfacial energy. Results indicate that Fe [110]/ HfC [100] interface is more stable than Fe [110]/ TMC [100] ( TM = Ti and Zr ). The analysis of different tensile fracture processes shows that the misfit dislocations play an important role in the fractures of interfaces between iron and transitional metal carbides.

Critical sizes for the stabilization of coherent precipitates

On growth of a precipitate beyond a critical size (r*), interfacial misfit dislocation loops are energetically stabilized. In the case of precipitation in (small) finite crystals, the energy of both the coherent precipitate and the dislocation loop are altered with respect to bulk crystals. Thus, as the crystal (domain) size approaches nanoscale, the critical size (r*) is expected to be altered with respect to bulk crystals. In the current investigation, finite element simulations are performed to study the variation of critical size (r*) with crystal/domain size and it is shown that below a critical domain size, the coherent precipitate is stabilized. Important findings include: (i) strain energy versus precipitate-size plot shows change in curvature for large precipitate sizes and (ii) coherent state is stable in two distinct regimes of precipitate sizes. Further, a phase diagram showing the stability regions of the coherent and semi-coherent states of the precipitate is drawn.

Molecular dynamics simulations of plastic deformation in Nb/NbC multilayers

Experimental studies show that metal–ceramic multilayers can have high strength, high strain hardening and measurable plasticity when the ceramic layer is a few nanometers thick. Using molecular dynamics simulations we studied deformation mechanisms in metal–ceramic multilayers and the role of interface structure and layer thickness on mechanical behavior. NbC/Nb multilayers were investigated numerically using the molecular dynamics (MD) method with empirical interatomic potentials. The interface dislocation structure was characterized by combining MD simulations and atomically informed Frank–Bilby theory. Two sets of pure edge misfit dislocations have been identified. Plastic deformation in NbC/Nb multilayers commences first in the metal layers by nucleation and glide of lattice dislocations initiating from interface misfit dislocations. These dislocations glide in the Nb layer and are deposited at the interface. The deposited dislocations facilitate slip transmission from the Nb layer to the NbC layer. The critical strain corresponding to dislocation nucleation is insensitive to layer thickness but depends on interface dislocation structure. The strain hardening and the peak flow strength of NbC/Nb multilayers are associated with the slip transmission from Nb to NbC, and are correlated to the interfacial dislocations, Nb layer thickness, and NbC layer thickness. The flow strength decreases with increasing Nb layer thickness and decreasing the NbC layer thickness.

OS0309 分子動力学法によるバンプと基板の界面特性評価

In this study, singular stress at corners in an anisotropic two-dimensional joint structure under a tensile loading is analyzed using molecular dynamic (MD) method and the anisotropic elasticity theory. The analysis of stress fields near interface misfit dislocation in a two-phase anisotropic body considering interface stress and interface elasticity. The displacement and stress distributions at the interface are compared the analysis considering the interface properties and the MD method.

Critical sizes for coherent to semicoherent transition in precipitates

Abstract A coherent precipitate, on growth beyond a critical size, can become semicoherent through the formation of interfacial misfit dislocations. This investigation pertains to the finite element simulation of the state of stress of a coherent precipitate, its growth and the change in state of stress on the formation of an interfacial misfit dislocation loop. Critical radii are determined from the simulations based on: (i) global energy minimum (r*) and (ii) local force balance along the radial direction (r c). The concept of local force balance as existing in literature is extended to the circumferential direction, to calculate a new critical size (r t). Local force balance gives radii at which the interface is the stable position for the dislocation loop. Off-interface stability of the dislocation loops is also investigated. The Cu–γFe system is used as an example to illustrate the new methodology developed and validate the results of the simulation. The power of the methodology is shown by considering a configuration (precipitation in a thin disc), where standard theoretical formulations are inadequate.

Anomalous strain behavior on EuTe self-assembled islands

EuTe is a magnetic semiconductor with potential applications in prototype optoelectronic and spintronic devices. In this work, we investigated the structural properties of EuTe grown on BaF2(111) substrates by molecular beam epitaxy. X-ray diffraction measurements were performed on two series of samples with different growth times and temperatures. The growth occurs in the Volmer-Webber mode, with initial formation of islands that then coalesce to form thin films. The islands size, mosaic spread, and strain state are deduced as a function of growth conditions. Surprisingly, the EuTe islands exhibit in-plane tensile strain, while compressive strain is expected for structures grown over a substrate with smaller lattice parameter. The islands tensile strain relaxes with increasing deposition times and substrate temperature, and it tends to zero for thick EuTe films. We propose that the EuTe/BaF2 lattice mismatch is compensated by the formation of interfacial misfit dislocations. The growth conditions out of equilibrium favor the formation of a metastable state with a high concentration of dislocations that over-compensates the original misfit. This is in agreement with the observed reduction of tensile strain as the substrate temperature increases.

Calculation of the bending area of threading dislocations of InGaAs quantum dots on a GaAs substrate

An equilibrium approach is used to calculate the strain energy of InGaAs/GaAs quantum dots (QDs) before and after the onset of bending of threading dislocation (TD) into interfacial misfit dislocation (MD). The energy balance method is adopted to predict critical conditions for TD bending. We find that the critical bending area in which the inclination of TD is energetically favorable depends strongly on the QD component. The results provide guidelines for the design of quantum dot dislocation filter.

TEM Characterization of HgCdTe/CdTe Grown on GaAs(211)B Substrates

A microstructural study of HgCdTe/CdTe/GaAs(211)B and CdTe/GaAs(211)B heterostructures grown using molecular beam epitaxy (MBE) was carried out using transmission electron microscopy and small-probe microanalysis. High-quality MBE-grown CdTe on GaAs(211)B substrates was demonstrated to be a viable composite substrate platform for HgCdTe growth. In addition, analysis of interfacial misfit dislocations and residual strain showed that the CdTe/GaAs interface was fully relaxed except in localized regions where GaAs surface polishing had caused small pits. In the case of HgCdTe/CdTe/GaAs(211)B, the use of thin HgTe buffer layers between HgCdTe and CdTe for improving the HgCdTe crystal quality was also investigated.

Residual stresses in thin film systems: Effects of lattice mismatch, thermal mismatch and interface dislocations

This paper explores the mechanisms of the residual stress generation in thin film systems with large lattice mismatch strain, aiming to underpin the key mechanism for the observed variation of residual stress with the film thickness. Thermal mismatch, lattice mismatch and interface misfit dislocations caused by the disparity of the material layers were investigated in detail. The study revealed that the thickness-dependence of the residual stresses found in experiments cannot be elucidated by thermal mismatch, lattice mismatch, or their coupled effect. Instead, the interface misfit dislocations play the key role, leading to the variation of residual stresses in the films of thickness ranging from 100nm to 500nm. The agreement between the theoretical analysis and experimental results indicates that the effect of misfit dislocation is far-reaching and that the elastic analysis of dislocation, resolved by the finite element method, is sensible in predicting the residual stress distribution. It was quantitatively confirmed that dislocation density has a significant effect on the overall film stresses, but dislocation distribution has a negligible influence. Since the lattice mismatch strain varies with temperature, it was finally confirmed that the critical dislocation density that leads to the measured residual stress variation with film thickness should be determined from the lattice mismatch strain at the deposition temperature.

Determining the Burgers vectors and elastic strain energies of interface dislocation arrays using anisotropic elasticity theory

A formalism for describing interface dislocation arrays linking the Frank–Bilby equation and anisotropic elasticity theory under the condition of vanishing far-field stresses is developed. The present approach enables the determination of a unique reference state for interface misfit dislocations, within which the Burgers vectors of individual dislocations are defined and allows for the unequal partitioning of elastic fields between neighboring crystals. The elastic strain energies of interface dislocation arrays are computed using solutions for short-range elastic fields. Examples of applications to simple interfaces are given, namely symmetric tilt and twist grain boundaries, as well as a pure misfit heterophase interface.

Edge misfit dislocations in core–shell nanowire with surface/interface effects and different elastic constants

A model of the generation for an edge misfit dislocation in the system of a nanowire surrounded by a co-axial film with surface/interface effects is investigated. The critical conditions of an edge misfit dislocation formation at the interface are analyzed, under considering the influence of the material elastic dissimilarity, misfit strains, the radius of the nanowire, core radius of the misfit dislocation and the surface/interface effects. The results show that the critical film thickness reduces with increment of the misfit strains, nanowire radius and core radius of the edge misfit dislocation, below the critical values of which, the misfit dislocation is energetically unfavorable whatever the film thickness. Critical film thickness first decreases and then increases with increasing the ratio of the shear modulus. There exists a critical film thickness below which no interfacial misfit dislocation could be introduced whatever the ratio of the shear modulus. There also exists a critical value of the ratio of the shear modulus, above which edge misfit dislocation does not form at any film thickness. The negative (positive) surface/interface stress can decrease (increase) the formation energy of the edge misfit dislocation. The positive (negative) surface/interface stress would increase (decrease) the critical film thickness, critical misfit strains and critical nanowire radius. The positive (negative) surface/interface stress would decrease (increase) the range of the film thickness and the critical ratio of the shear modulus. The larger the values of the surface/interface stress qualities, the greater the influence of the surface/interface stress on critical parameters.

Atomistic modeling of the interaction between matrix dislocation and interfacial misfit dislocation networks in Ni-based single crystal superalloy

To reveal the intrinsic strengthening mechanism in Ni-based single crystal superalloy, the interaction between matrix dislocations and interfacial misfit dislocation networks was modeled in this contribution via molecular dynamics (MD) method. Our results show that the role of interfacial dislocation networks is very complex. On the one hand, the interfacial dislocation networks can act as dislocation sinks to absorb/accommodate the matrix dislocations. During the accommodation process of matrix dislocation by the networks, both the interfacial Lomer–Cottrell locks and a[100] dislocation junctions are formed, which stabilize and strengthen the interfacial dislocation networks. On the other hand, the interfacial dislocation networks can provide dislocation pins to prevent the matrix dislocations from cutting into the γ′ precipitate. These matrix dislocation segments pinned at the phase interface can serve as Frank–Read sources with their length being about half of the dislocation network spacing, providing an explanation for the effect of dislocation network spacing on the creep strength of the Ni-based single crystal superalloy.

Position dependant critical thickness in finite epitaxial systems

During the growth of an epitaxial overlayer, interfacial misfit dislocations become energetically favourable on exceeding the critical thickness. In the case of finite systems (i.e. either the substrate or the epitaxial overlayer is finite), different positions along the interface are not equivalent and the critical thickness will be position dependent. Minimum of these thickness values can be visualized as the global critical thickness. The current work aims at simulating the stress state of a growing epitaxial overlayer on a finite substrate using finite element method and further use the numerical model to calculate the position dependent critical thickness along the interface. Eigenstrains will be imposed in selected regions in the domain towards this end. The variation of shear stress along the interface will be computed from the model to understand the issues related to the mechanism of formation of misfit dislocations. This includes the important question: “why interfacial dislocations cannot ‘punch-in’ directly from the free lateral surface?” The simulation methodology and associated concepts can readily be extended to other finite epitaxial systems like stripes and islands.

Spectral and Transient Luminescence Measurements on GaSb/AlGaSb Quantum Wells Grown on GaSb/GaAs Heterojunctions with and without Interfacial Misfit Arrays

Growth of 90° interfacial-misfit-dislocation (IMF) array at heterointerfaces offers low dislocation densities in highly mismatched heterostructures such as GaSb/GaAs. We investigated time-integrated and time-resolved photoluminescence (PL) properties of a GaSb/AlGaSb quantum well (QW) structure grown on (001) GaAs substrate with and without IMF array at the GaSb-buffer/GaAs interface. Our observation reveals that the low-temperature PL from the QW with IMF is twice more intense than that of the QW without IMF, indicating higher quantum efficiency with IMF. The QW with IMF also exhibited the band filling effect at higher excitation power revealed from the spectrally resolved PL decay measurements. These results are the indication of subdued dislocation density with the IMF growth mode. Our PL measurement results along with supportive band-structure calculation of the GaSb/AlGaSb QW show that the luminescence efficiency of the present QW structure is limited by the hole leakage at elevated temperature. Therefore the IMF effect will be more clearly demonstrated by replacing the heterostructure with the one with higher band-offsets.

Interphase Defects, Structures, and Phase Stability

Interface is defined as a common boundary of two spaces or phases. In solid-state materials, this usually means a two-dimensional defect that separates two regions of otherwise perfect bulk, and sometimes it goes to three dimensional, e.g., in the case of diffuse interface or disconnections. In general, the different bulk regions surrounding the interface can be different materials or crystal phases, so these interface boundaries can be called interphase boundaries. Solid-state materials with abundant internal interfaces may possess unusual physical properties or functionalities. This promising opportunity motivates many research studies, both experimental and theoretical in nature, geared toward incorporating knowledge of atomic-level structure and properties of interfaces into mechanistically informed interface design of materials. The unusual physical properties caused by interfaces include, for example, extraordinary radiation damage resistance and mechanical behaviors. The physical basis behind these extraordinary performances of materials is due to the fact that the interfaces can interact with point defects and dislocations in a strong manner. Understanding of the detailed mechanisms, including thermodynamic and kinetic factors at atomistic levels, is thus very important. The characterization of interface structures is a foundation step in the understanding. Additionally, how the stability of phases maybe affected by external driving forces is also of high importance because it is desired to keep the phases stable so the performance of materials maybe sustainable. Five articles are included in this issue representing some of the recent research efforts in understanding interphase defects, structures, and phase stabilities in different perspectives. The first article by X.M. Bai and B.P. Uberuaga gives a review of atomistic simulation works that examined the influence of grain boundaries, which are of the homophase interface boundary type, on the defects production during collision cascades. Collision cascade is a set of atomic collision events induced by energetic particles in material when the material is under irradiated conditions. Radiation damage is of great concern for materials in nuclear energy applications and is connected directly to the defect production in collision cascade processes. Atomistic simulation studies demonstrated that grain boundaries absorb more interstitials than vacancies during collision cascades. The absorbed interstitials can also spontaneously emit from interfaces to annihilate vacancies in the nearby bulk. The grain boundaries also disrupt the channeling effect in collision cascades, thus reducing cascade sizes. As a result, the number of defects produced is also lowered. Several different materials including face-centered cubic (fcc) Ag, Ni, Cu, bodycentered cubic (bcc) Fe, UO2, TiO2, and SiC were examined. And it was noted that the influences of grain boundaries are also sensitive to the type of materials. These atomistic simulation results provide an improved understanding of how interfaces may influence radiation damage evolution in materials. The second article by K. Kolluri et al. focuses on a research summary of the behavior of vacancies and interstitials at heterophase fcc-bcc semicoherent interfaces. Experimentally, nanolayered fcc-bcc composites such as Cu-Nb exhibit significantly enhanced radiation-damage tolerance as compared to monolithic metals. Knowledge of defects behavior at interfaces is essential for the understanding of such effects as well as other material properties such as creep and swelling. Using atomic-scale simulations, it is found that the formation, migration, and clustering of interfacial vacancies and interstitials at Cu-Nb KS interfaces is determined by the structure of these interfaces, which can be described with ordered arrays of misfit dislocations. In addition, the migration of defects at the interfaces is through a mechanism that depends on interfacial misfit dislocation properties and can be described using dislocation mechanics. To systematically test the effect of bonding and lattice parameter on point defect behavior, potentials were ‘‘tuned’’ by changing either the dilute of heats of mixing between Cu and Nb or the Xiang-Yang (Ben) Liu is the guest editor for the Chemistry and Physics of Materials Committee of the TMS Structural Materials Division, and coordinated the topic Interphase Defects, Structures, and Phase Stability in this issue. JOM, Vol. 65, No. 3, 2013

A rate theory study of helium bubble formation and retention in Cu–Nb nanocomposites

A spatially dependent rate theory model for helium migration, clustering, and trapping on interfaces between Cu and Nb layers is introduced to predict the evolution of the concentrations of He clusters of various sizes during implantation and early annealing. Migration and binding energies of point defects and small clusters in bulk Cu and Nb are found using conjugate gradient minimization and the nudged elastic band method. This model is implemented in a three-dimensional framework and used to predict the relationship between helium bubble formation and the nano-composite microstructure, including interfacial free volume, grain size, and layer thickness. Interstitial and vacancy-like migration of helium is considered. The effects of changing layer thickness and interfacial misfit dislocation density on the threshold for helium bubble nucleation are found to match experiments. Accelerated helium release due to interfaces and grain boundaries is shown to occur only when diffusion rates on interfaces and grain boundaries are greatly increased relative to the bulk material.

Finite Substrate Effects on Critical Thickness in Epitaxial Systems

During the growth of an epitaxial overlayer on a thick substrate (GeSi on Si), an interfacial misfit dislocation becomes energetically favourable on exceeding the critical thickness. In substrates of finite thickness, the value of critical thickness is altered with respect to thick substrates. Thin substrates can bend and partially relax the coherency stresses, thus contributing to the altered value of the critical thickness. The current work aims at simulating the stress state of a growing finite epitaxial overlayer on a substrate of finite thickness, using finite element method. The numerical model is used to calculate the critical thickness for substrates with finite thickness. Eigenstrains will be imposed in selected regions in the domain towards this end. Size of the substrate for which it is not energetically favourable to accommodate a misfit dislocation is determined from the simulations (i.e. the system remains coherent for substrates below this thickness). Important effects arising in the transition regime of substrate thicknesses are also investigated.

Comparison of microstructure of N-polar GaN/AlGaN/GaN heterostructures grown on different substrates

Several N-polar GaN/AlGaN/GaN heterostructures intended for high electron mobility transistor (HEMT) devices were grown by molecular beam epitaxy using either SiC or freestanding GaN substrates. The microstructure of these heterostructures has been compared using transmission electron microscopy and associated analytical techniques. Considerable 1:1 ordering was observed within the AlxGa1−xN layers (where x∼0.34–0.37) for both substrate types. Threading dislocations were the most common defects observed in structures grown on SiC substrates, whereas interfacial misfit dislocations and surface pits were the primary defects observed in samples grown on the freestanding GaN substrates.

Microstructure of epitaxial YBa2Cu3O7−δ thin films grown on Pb(Mg1/3Nb2/3)0.7Ti0.3O3 substrates

The microstructure of epitaxial c-axis oriented YBa2Cu3O7−δ (YBCO) thin films grown on piezoelectric/ferroelectric (001) Pb(Mg1/3Nb2/3)0.7Ti0.3O3 (PMN-PT) substrates by pulsed laser deposition has been studied using transmission electron microscopy. It is shown that major defects in the films are interfacial misfit dislocations and planar defects. Moreover, a small amount of a-axis oriented domains with inclined domain walls are observed in the YBCO films and the formation mechanism of the inclined domain walls is discussed. In addition, tiny precipitates near the interface are observed in some cases. All these defects and the domain structure contribute to the strain relaxation of the epitaxial YBCO thin films. These findings may be helpful for future research on correlation of microstructure and physical properties in the high-Tc superconductor–ferroelectric heterostructures.

Interfacial Edge Dislocation Interactions with Free-Surfaces in Nanocrystals

The configurational force experienced by a dislocation towards a free-surface is termed as the image force. In this work we consider a combination of two cases, wherein the image force experienced by an edge dislocation is considerably altered with respect to an edge dislocation in a semi-infinite body: (i) interfacial misfit edge dislocation in an epitaxial system and (ii) edge dislocation in a 2D nanocrystal. The interaction of an edge dislocation with a free-surface in a 2D nanocrystal can be: (i) attractive with a considerably altered magnitude and direction (as compared to the theoretically calculated value), (ii) neither attractive nor repulsive or (iii) even repulsive. To compute the image force on a misfit edge dislocation in a 2D nanocrystalline epitaxial system, a finite element model is constructed and stress-free strains are imposed in appropriate regions of the domain, to simulate an epitaxial system (Nb/Sapphire) and an interfacial dislocation. The results of the simulation are contrasted with the standard theoretical formulations, which are shown to be highly inadequate to handle such cases which involve epitaxial strains, two materials in the system and considerable domain deformations. Image Force, Finite Element Method, Interfacial Misfit Dislocation, Domain