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Abstract: It is well known that the structures and properties of ferroelectric films can be remarkably different from their bulk counterpart, and a nonlinear phenomenological theory of ferroelectrics is applied to study phase structures and electromechanical properties of epitaxial Pb(Zr1−x Ti x )O3 (PZT) thin films, focusing on the effects of substrate and film thickness. The effective misfit strain induced by lattice mismatch between film and substrate has been calculated, and the misfit strain–composition, temperature–composition, and thickness–composition phase diagrams of PZT films have been constructed. The temperature–composition phase diagram differs substantially from that of bulk PZT ceramics, and the calculated phase structures in thin films allow us to explain numerous previous experimental observations. In particular, it is confirmed that the morphotropic phase boundary (MPB) of PZT films is shifted from that of bulk PZT, resulting in substantially different electromechanical response in PZT thin films. Good agreement with experimental data is observed in general. [ABSTRACT FROM AUTHOR]

At the time of writing, data have been reported on several hundred different cuprate materials, of which a substantial fraction show superconductivity at temperatures as high as 130 K. The existence of several competing phases with comparable energy shows up in different ways in different materials, therefore it has not been possible to converge toward a universal theory for high- Tc superconductivity. With the aim to find a unified description the Aeppli–Bianconi 3D phase diagram of cuprates has been proposed where the superlattice misfit strain η is the third variable beyond doping δ and temperature T. The 3D phase diagrams for the magnetic order, and for the superconducting order extended to all cuprate families are described. We propose a formula able to describe the Tc ( δ, η) surface, this permits to identify the stripe quantum critical point at δc=1/8 and ηc=7% which is associated with the incommensurate to commensurate stripe phase transition, controlled by the misfit strain. [ABSTRACT FROM AUTHOR]

Abstract: A nonlinear phenomenological theory was described for the epitaxial BiFeO3 (BFO) thin films with single domain structure. With the consideration of the mechanical substrate effect, the “misfit strain–temperature” phase diagram is constructed for the BFO thin film by numerical calculations. It is found that the polarization instabilities result in the formation of new domain states forbidden in bulk crystals, which has been observed in the experiments. [Copyright &y& Elsevier]

A theoretical model was suggested which describes the generation of the misfit dislocation dipole in the system of the viscoelastic matrix containing a circular stiff nanoscale inhomogeneity. The critical condition of misfit dislocation dipole and the solution of equilibrium position were given. The influence of the ratio of shear modulus, the misfit strain and viscosity on the equilibrium of the dislocation and critical parameter of inhomogeneity was investigated. The result shows that the equilibrium position d e increases with the increase of the ratio of original shear modulus and the effect decreases with the increase of viscosity of matrix. Along with the increase of viscosity of matrix, d e first increases and then decreases and possesses maximum value when t=0.3 τ and tends to a stable value when t⩾1.0 z. Along with the increase of viscosity of matrix, R c first decreases and then increases and possesses minimum value when t=0.3 τ and tends to a stable value when t⩾1.0 τ. [ABSTRACT FROM AUTHOR]

We review the role that first-principles calculations have played in understanding the effects of substrate-imposed misfit strain on epitaxially grown perovskite ferroelectric films. We do so by analyzing the case of BaTiO3, complementing our previous publications on this subject with unpublished data to help explain in detail how these calculations are done. We also review similar studies in the literature for other perovskite ferroelectric-film materials. [ABSTRACT FROM AUTHOR]

Abstract: The formation of intragranular θ′ disk-shaped precipitates in Al–Cu alloys is accompanied by a thickness-dependent misfit strain. In this study, the lengthening rates of Widmanstätten θ′ precipitates of two different thicknesses (1.2 and 2.0nm) are compared. It is shown experimentally that the thinner precipitates grow more slowly than their 2.0nm thick counterparts. These observations are interpreted in terms of a model that includes the effects of capillarity and of misfit strain, as well as the effect of a misfitting solute (Cu) in the diffusion field in the parent crystal. [Copyright &y& Elsevier]

Thin films and multi-layered coatings comprised of different classes of materials are often used for various functional devices. The thermo-mechanical integrity of these systems is becoming a major concern and is strongly related to the residual stresses because of the fabrication processes. In this paper, the sources of the residual stresses in the coating-based systems and the concept of “misfit strain” were briefly reviewed. Analytical models were developed to predict the residual stresses in multi-layered film structures or coating-based systems using the force and moment balances. In addition, the residual stress distributions in the functionally and compositionally graded coatings were also analyzed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a relatively simplified model with the closed-solutions considering the edge effect was developed to predict the interfacial stresses and normal stresses within an elongated film strip/substrate system and the edge deflection of it. For the stresses at the interface and the normal stresses in the film, the analytical modeling results agreed well with the finite element results. Using this model, some obvious relationships between the material properties and the dimensions of the film and substrate and the edge deflection or interfacial stresses could be reflected. For a plasma sprayed coating-based system, the intrinsic stress had a significant contribution to the final stress, since it could alter the final residual stress state of the film. [Copyright &y& Elsevier]

For the first time we proved, that built-in electric field originated from film-substrate misfit strain suppresses the size-driven transition from ferroelectric to paraelectric phase in the strained ultrathin ferroelectric films. Instead of paraelectric phase built-in field induces electret-like polar state with irreversible spontaneous polarization, pyroelectric and piezoelectric response at film thickness below the critical one. This normal to the film surface field increases when the film thickness decreases. Built-in field makes spontaneous polarization orientations energetically non-equivalent, in particular spontaneous poling becomes the most probable for the thin enough film when it exceeds thermodynamic coercive field. So, mismatch-induced electric field is the most probable reason of self-polarization phenomenon and electret state appearance in ultrathin films. [ABSTRACT FROM AUTHOR]

We have investigated lattice instabilities of ultra-short period BaTiO 3 /SrTIO 3 (BTO/ STO) artificial superlattice (double-perovskite 10-atom unit cell) as a function of epitaxial strain using first-principles density functional theory (DFT) calculations based on pseudopotentials and a plane-wave basis. We find a structural transition from the tetragonal phase at compressive strain to the monoclinic phase at tensile strain. In the tetragonal phase, the Ti ions displacement patterns of the BTO/STO superlattice show ferrielectric phase behavior. Likewise, those of the monoclinic BTO/STO superlattice along [001] direction are very similar to the tetragonal BTO/STO superlattice. However, the displacement patterns in the xy -plane BTO/STO superlattice exhibit different behavior which both Ti ions displace parallely along [110] direction and against direction of oxygen displacements. It means that the monoclinic phase of BTO/STO superlattice is ferrielectric along [001] direction similar to tetragonal BTO/STO superlattice, but is ferroelectric in the xy- plane. [ABSTRACT FROM AUTHOR]

Abstract: Large angle convergent beam electron diffraction (LACBED) has been used to examine AlGaN epilayers grown by facet-controlled epitaxial lateral overgrowth on GaN/(0001) sapphire substrates in prototype UV laser structures. The substrates, defined by masks with seed openings along a stripe direction, had GaN seed columns with surfaces. Studies were carried out on cross-sectional samples cut perpendicular to the stripe axis. An LACBED analysis of the orientation of (000 2) planes, and of the planes parallel to the stripe axis, revealed that the AlGaN wings were both rotated by angles of 1–2×10−2 radians about the stripe axis with respect to the underlying GaN, and distorted due to misfit strains. It is shown that the results are consistent with the observed structure of the AlGaN/GaN and the wing/wing boundaries, and with a new model for the generation of a-type misfit dislocations at the AlGaN/GaN interface. [Copyright &y& Elsevier]

Strain-mediated growth of two-dimensional (2D) islands deposited coherently on the surface of an elastically isotropic substrate is studied. From an energetic consideration, it is shown that the island edge is unstable when the island grows to a critical size. The instability is explained as a trigger of island ramifying and splitting observed in experiments. To have a closer look at the dynamic aspects of island growth, a numerical simulation based on phase field method is also performed. The result is consistent with our energetic analysis. [Copyright &y& Elsevier]

The misfit between an epilayer and a substrate may be accommodated by misfit dislocations (MDs) or misfit strain (MS) or both. In a small misfit system the misfit is accommodated by MS alone up to a critical thickness whereafter the residual MS decreases as the thickness increases. The main objective of this paper is to review theoretical work aimed at understanding MS relief in a growing epilayer by the introduction of MDs, with the view of resolving the discrepancies between predicted and observed critical thickness and residual MS after onset of MS relief. Since the predictions are based on equilibrium principles, equilibrium theories for monolayers (MLs) in the Frenkel-Kontorowa model, and for thickening epilayers (growing ML-by-ML) in the Volterra model, are briefly summarized, including some consideration of the conditions for ML-by-ML growth. Since equilibration can be drastically retarded by barriers to nucleation and motion of dislocations the observed quantities are most often non-equilibrium values. Calculations show (i) that MD sources are normally needed to the onset of MS relief, (ii) that threading dislocations are the 'softest' sources, (iii) that even with threading dislocation sources MS relief may lag behind equilibrium predictions and (iv) that Peierls friction may lead to an infinitely large critical thickness. [ABSTRACT FROM AUTHOR]

Van der Waals heterostructures inherit many novel electronic and optical properties from their constituent atomic layers. Mechanical stability is key for realizing high-performance nanodevices based on van der Waals heterostructures. However, buckling instability is a critical mechanical issue for heterostructures associated with its two-dimensional nature. Using molecular dynamics simulations of graphene/MoS 2 heterostructures, we demonstrate the relationship between buckling instability and the misfit strain that arises inevitably in such heterostructures. The impact of misfit strain on buckling depends on its magnitude: (1) A negative misfit strain causes a pre-compression of the graphene layer, which in turn initiates and accelerates buckling in this layer and reduces the buckling stability in the heterostructure as a whole. (2) A small positive misfit strain enhances the buckling stability of the graphene/MoS 2 heterostructure by pre-stretching and hence decelerating the buckling of the graphene layer (where heterostructure buckling is initiated). (3) In the case of a large positive misfit strain, the graphene layer is pre-stretched while the MoS 2 layer is significantly pre-compressed, so that heterostructure buckling is initiated by the MoS 2 layer. Consequently, the buckling stability of the graphene/MoS 2 heterostructure is reduced by increasing the large positive misfit strain. These findings are valuable for understanding the mechanical properties of van der Waals heterostructures., (© 2021 IOP Publishing Ltd.)

[Display omitted] • MD simulations show islands grow during liquid phase epitaxy of aluminum. • Islands relieve strain, while maintaining coherency with lattice mismatched substrates. • Thermodynamic analysis captures reduced undercooling for island versus planar growth. • Islands are transient and subsequent misfit dislocations permanently relieve misfit. • Being as small as 10 nm, this mechanism can activate inoculants within a melt. Liquid phase epitaxy of aluminum on substrates of varying lattice spacing is investigated. Molecular dynamic simulations show the formation and growth of small (nm to µm) islands following a Stranski-Krastanov mode, where a few unit cell thick, solid layer first templates to the substrate. Subsequent island formation reduces the strain energy within the nucleating solid. Growing islands coalesce upon impinging, while misfit dislocations form during growth and remain at the substrate interface. A thermodynamic analysis reveals island creation is a stochastic process, requiring thermal energy to overcome an activation barrier. Relative to a planar growth criterion, island growth becomes the prominent mechanism at moderate lattice mismatch between the solid and substrate. The difference in activation undercooling between the two growth mechanisms increases with mismatch magnitude. The presented model is used to evaluate island growth for other metals, and can be used as a criterion for activation of a catalyzing surface. [ABSTRACT FROM AUTHOR]

We investigated the precipitation behavior and mechanical properties of naturally aged Al–7.6Zn–2.7Mg–2.0Cu–0.1Zr–0.07Ti (wt.%) alloy using various experimental methods including electron backscatter diffraction, microhardness, electrical resistivity, differential scanning calorimetry, X-ray diffraction, transmission electron microscopy (TEM), atom-probe tomography (APT), and tensile tests. GPI zones commenced forming after 0.5 h of natural aging and increased in volume fraction during further aging. GPII zones were observed in alloys that were naturally aged longer than 1500 h at 25 °C. The APT and TEM analyses identified blocky GPI zones and elongated GPII zones on the {111} Al planes in the alloy that were naturally aged for 1500 h. The compressive lattice strains of the GPI and GPII zones were ~2.6 and ~7.8%, respectively, at the centers of the zones. For the GP zones, the Zn/Mg atomic ratio was ~1.2, the mean radius 0.76 nm, the number density 3.22 × 1024 m−3, and volume fraction 0.58%. Yield strength modeling, strain hardening behavior, and fractured morphology analyses indicated that the improved strength from natural aging was due to the coherency plus modulus mismatch strengthening of the GP zones, which had an average misfit strain of ~4%. [ABSTRACT FROM AUTHOR]

In the present work, the effect of a pre-existing nanovoid on multivariant martensitic growth and in particular, on the phase transformation (PT) threshold stress, is investigated using the phase field approach. In order to create a pre-existing nanovoid in the model, a single nanovoid has been stabilized in the center of the computational domain using a phase field approach. The coupled Ginzburg-Landau and elasticity equations are solved to capture the evolution of martensitic nanostructure. The above systems of equations are solved using the finite element approach and the COMSOL code. Nanovoid-induced two variant martensitic growth under negative pressure is studied in detail. The PT threshold stress is found for different nanovoid misfit strain constants and different temperatures. The PT threshold stress increases linearly by increasing the temperature for any misfit strain which rate of increase is found the same for any misfit strain. For any temperature, the PT threshold stress nonlinearly decreases as the misfit strain constant increases. Under the applied negative pressure, both the first and the second variants grow from the nanovoid surface which evolutions are explained based on the distributions of the stress and transformation work. The martensitic growth is more pronounced for larger misfit strains due to higher stress concentrations. The martensitic nanostructure, stress distribution and the PT threshold stress are also found in the presence of a nano-hole for different temperatures and are compared to those of the nanovoid. The martensitic growth is also studied for different temperatures. As the temperature increases, the growth is slower and this is explained using the phase concentration for both the first and the second variants which increases nonlinearly and its growth rate nonlinearly varied vs time for any temperature. For larger temperatures, the phase concentration decreases and the growth rate decreases at the same phase concentration. A larger negative pressure is required for the martensitic growth at larger temperatures. The effect of sample size on the PT threshold stress was also investigated. The effect of mechanical driving force on the nanovoid-induced martensitic growth is studied by applying different negative pressures. As the negative pressure increases the growth exceedingly increases. The phase concentration evolution reveals the dependence of the growth on the loading magnitude so that for any loading, the phase concentration increases nonlinearly with a nonlinearly variable growth rate. As the loading increases, the phase concentration increases and the growth rate increases at the same phase concentration. Applying uniaxial loading results in nanovoid-induced single variant martensitic growth for which the PT threshold stress almost linearly decreases as the misfit strain constant increases. Comparing the results of the uniaxial loading and negative pressure shows that the PT threshold stress under uniaxial loading is approximately 1.6 times smaller than that under negative pressure for any misfit strain. The presented model and the obtained results will help to develop an interaction model between nanovoids and multiphase structure at the nanoscale. Image 1 • The effect of a pre-existing nanovoid on martensitic growth and the PT threshold stress is investigated using the PFA. • The PT threshold stress is found for different nanovoid misfit strain constants and different temperatures. • The PT threshold stress increases linearly by increasing the temperature for any misfit strain. • For any temperature, the PT threshold stress nonlinearly decreases as the misfit strain constant increases. • The growth of both variants from the nanovoid surface under negative pressure is explained based on the transformation work. • The martensitic growth is also studied for different temperatures and udder different biaxial tensions. • Applying uniaxial loading results in nanovoid-induced single variant martensitic growth. [ABSTRACT FROM AUTHOR]

Abstract: Using an atomistic shell model we study the temperature dependence of the ferroelectric properties of under biaxial compressive strain applicable to growth on perovskites substrate. Molecular dynamics simulations show a “” sequence of phase transitions when temperature is increased, and the absence of an “ phase”. The first-order paraelectric-to-ferroelectric phase transition presents in bulk changes to a second-order one as a consequence of the in-plane constraint imposed by the mechanical boundary conditions. From the tetragonal ferroelectric phase, the transition takes place in a finite range of temperature where the lattice parameter normal to the plane keeps approximately constant until is reached. Analysis of the local polarization behavior reveals an order–disorder dynamics as the dominant mechanism of the transition. [Copyright &y& Elsevier]

For any misfit strain, the effect of nanovoid on the PT is more pronounced for larger temperatures. The nanovoid-induced martensitic growth is explained based on the distributions of the stress and transformation work. The martensitic growth is studied for different temperatures and different mechanical driving forces. • Effect of nanovoid on martensitic growth under uniaxial stress is studied via PFA. • PT threshold stress is found for different nanovoid radii, strains and temperatures. • The dependence of the misfit strain on the nanovoid radius is considered. • The PT threshold stress linearly increases as the temperature increases. • The PT threshold stress exponentially reduces as the nanovoid radius increases. • Neglecting size dependence of misfit strain gives a smaller PT threshold stress. • Effect of nanovoid on the PT is more pronounced for larger temperatures. • Martensitic growth is explained based on stress and transformation work. • Martensitic growth is studied for different temperatures and mechanical loadings. In the present work, the effect of a pre-existing nanovoid on martensitic growth under uniaxial stress in NiAl is investigated using the phase field theory. In order to create a pre-existing nanovoid in the model, a single nanovoid has been stabilized in the center of the computational domain using a phase field approach. The coupled system of Ginzburg-Landau and elasticity equations are then solved for the evolution of martensitic nanostructure in the presence of the obtained nanovoid. The finite element approach and the COMSOL code are used to solve the above systems of equations. Even though the Ginzburg-Landau model includes two martensitic variants, only the first variant grows under uniaxial stress. The phase transformation (PT) threshold stress is found for different nanovoid radii and different temperatures. The dependence of the misfit strain on the nanovoid radius is considered which results in proper surface stress. The PT threshold stress linearly increases as the temperature increases for any nanovoid radius. The effect of temperature on the PT is found more pronounced for smaller nanovoids. It is also revealed that the PT threshold stress exponentially reduces as the nanovoid radius increases, in agreement with previous experimental/molecular dynamics results. Neglecting the size dependence of the misfit strain leads to a smaller PT threshold stress especially for lower temperatures and larger radii. For any misfit strain, the effect of nanovoid on the PT is more pronounced for larger temperatures. Under the uniaxial stress, the first variant started to grow vertically from the upper and lower surfaces of the nanovoid which evolution is explained based on the distributions of the stress and transformation work. The martensitic growth is more pronounced for larger radii. The martensitic growth is also studied for different temperatures. As the temperature increases, the growth is slower and this is explained using the phase concentration and its time rate. As the temperature increases, the phase concentration decreases and the growth rate decreases at the same phase concentration. The stress and transformation work distributions for different temperatures and their corresponding PT threshold stresses for a constant radius are studied for the earlier stage of growth. As the temperature increases, a larger uniaxial stress is required for the martensitic growth. The effect of mechanical driving force on the nanovoid-induced martensitic growth is studied by applying different uniaxial tensions. As the loading increases, the phase concentration increases and the growth rate increases at the same phase concentration. The obtained results allow for a better interpretation of the effect of nanovoids on the PT at the nanoscale and will help to develop an interaction model between nanovoids and multiphase structure at the nanoscale. [ABSTRACT FROM AUTHOR]

A novel Calphad coupled mechano-chemical phase-field model is presented which in addition to chemo-elastic contributions to the driving force further includes mechano-chemical effects on diffusion (stress-driven diffusion), equilibrium compositions and driving force. These effects have their origin in the concentration dependency of the eigenstrains and can significantly influence the phase transformation kinetics, especially in Ni-based superalloys where the different dissolved elements have strongly different partial molar volumes. In this paper, all mechano-chemical contributions to diffusion, equilibrium concentrations and driving force are derived starting from a free energy functional. In order to use the model in conjunction with Calphad databases, elastic effects are incorporated in an efficient and consistent way by a posteriori treatment of the chemical quasi-equilibrium data. The new model is first applied to evaluate the 3D-equilibrium shape of a single γ'-particle in a binary Ni-Al and a ternary Ni-Al-Mo alloy and then for the simulation of Ostwald ripening and rafting of the multicomponent CMSX-4 alloy. Results from simulations with and without consideration of the mechano-chemical contributions are compared. It is shown that, especially in case of the ternary and multicomponent alloys, the mechano-chemical effects on the equilibrium shapes of the γ'-particles and on interface kinetics are considerable and cannot be neglected. Moreover, different standard homogenization assumptions for stresses and strains inside the diffuse interface region (Voigt-Taylor, Khachaturyan, Reuss-Sachs) have been systematically compared and analyzed using an extended quasi-equilibrium approach, leading to a new evaluation of their applicability in the context of mechano-chemical coupling. [ABSTRACT FROM AUTHOR]

• An energy-based stability analysis of misfit dislocations in two-phase particles • Numerical calculation of phase transformation induced stresses and image forces • Examination of energetics of a misfit dislocation in LiFePO 4 particles • Prediction of unstable misfit dislocations below a critical particle size • Numerical estimates of critical size for different particle/interphase orientations It is well known that cycling induced capacity fading in phase transforming intercalation materials is critically linked to the severity of misfit strain between the phases which could result in the emergence of a variety of defects in the material. Here, adopting a planar model and making use of a well-established energy-based framework, we examine stability of a misfit dislocation lying at the phase boundary within a two-phase electrode particle. Within this framework, the stability criterion emerges as a result of competition between the work that must be done against the image forces with the work that is supplied by the phase transformation induced stresses, as the dislocation is pulled from free surface of the solid toward interior. A numerical model accounting for anisotropy of both misfit strain between the phases and elastic properties of the solid is developed. The model is in particular applied to the electrode particles of LiFePO 4 , a highly promising cathode material for lithium-ion battery applications in which misfit dislocations as a result of phase transformation have also been experimentally observed. The analysis is revealing of size effects on the stability of a misfit dislocation in the electrode particle. Most notably, it is shown that below a critical particle size, no misfit dislocation at the interphase can remain stable within the particle as it becomes energetically more favorable for the dislocation to be driven out of the particle through absorption by the free surfaces. Numerical estimates of the critical size are presented and discussed with reference to available experiments. Through providing a guideline for suppressing misfit dislocations, results of this work could have potentially important implications for disabling a wide range of dislocation-based fatigue mechanisms which could otherwise become active and result in capacity fading upon a large number of cycles. Image, graphical abstract [ABSTRACT FROM AUTHOR]