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The misfit strain within the core of a two-phase free-standing core–shell nanowire resulting in the generation of an edge misfit dislocation or an edge misfit dislocation dipole at the core–shell interface is considered theoretically within both the classical and surface/interface elasticity approaches. The critical conditions for the misfit dislocation generation are studied and discussed in detail with special attention to the non-classical surface/interface effect. It is shown that this effect is significant for fine cores of radius smaller than roughly 20 interatomic distances. The positive and negative surface/interface Lame constants mostly make the generation of the misfit dislocation easier and harder, respectively. Moreover, the positive (negative) residual surface/interface tensions mostly make the generation of the misfit dislocation harder (easier). The formation of individual misfit dislocation is energetically more preferential in finer two-phase nanowires, while the formation of misfit disl...

The (1 0 0) oriented (Pb,Sr)TiO3 (PST) thin films were prepared using terbium-doped lead titanate as inducing layer. Misfit strain of the PST thin films changed gradually along direction of thickness and with different compositions. Controlled by the strain, the Curie temperature was independent of the composition of the PST and the width of the Curie peak was broadened. The as-prepared PST thin films exhibited stable high dielectric tunability which was almost independent of composition as well as applied temperature. With the composition of PST changing from PST35 (PbxSr1−xTiO3 x = 0.35) to PST50, the room temperature tunability of the PST thin films maintains a stable value of about 40%. At a high applied temperature of 200 °C, the PST thin films still show a high tunability of about 35%. The strain-assisted control of the Curie temperature and the Curie peak width is attractive in designing high stable devices with high dielectric tunability.

The formation of isolated circular islands submitted to misfit strain has been theoretically investigated on the surface of a thin wetting layer of constant thickness deposited on a substrate by calculating the chemical potential of the island atoms. It is found that the island size selected by the misfit strain depends on the difference between the shear moduli of the islands (and wetting layer) and the substrate. An analytical expression for the island radius is derived from the first order development in the shear modulus difference.

Semicoherent interfaces containing discrete dislocations are more energetically favorable than those containing continuous distributions because of lower chemical energy. The classical Frank-Bilby theory provided a way to determine the interface Burgers vectors content but could not effectively predict the characteristics of discrete dislocations. Atomistic simulations provide insights into analyzing the characteristics of discrete dislocations but the analysis is often disturbed by the reaction of interface dislocations. By combining the classical Frank-Bilby theory and atomistic simulations, an atomically informed Frank-Bilby theory proposed in this work can overcome shortcomings in both the classic Frank-Bilby theory and atomistic simulations, and enable quantitative analysis of interface dislocations. The proposed method has been demonstrated via studying two typical dissimilar metallic interfaces. The results showed that Burgers vectors of interface dislocations can be well defined in a Commensurate/Coherent Dichromatic Pattern (CDP) and the Rotation CDP (RCDP) lattices. Most importantly, the CDP and RCDP lattices are not simply a geometric average of the two natural lattices, that is the lattice misfit and the relative twist take the nonequal partition of the misfit strain and the twist angle.

Lattice-mismatched heteroepitaxial growth in compound semiconductor layer structures, e.g. metamorphic buffers, is frequently used to combine materials with favorable properties. A detailed understanding of the strain relaxation during growth is important to optimize the buffer layers and to achieve high material quality. We present a method to determine the epilayer relaxation at growth temperature from room temperature X-ray diffraction measurements. For this the lattice parameters are measured with (004) and (224) reciprocal space maps along two orthogonal directions to account for anisotropic misfit strain relaxation. Dissimilar thermal expansion coefficients of substrate and epilayer are taken into consideration when calculating the lattice parameters and epilayer relaxation parameters at growth temperature. The application of this method is discussed for GaAs x P 1− x metamorphic buffer structure on Si with eight lattice-mismatched layers showing a relaxation parameter of over 130% at room temperature. All layers were found to be nearly 100% relaxed at growth temperature. The use of this method for other compound semiconductors is discussed.

This article clarifies a geometric method for calculating interfacial dislocation structures, to provide virtually unique initial dislocation structures for further relaxation. Ambiguities in specifying the misfit deformation and Burgers vectors are effectively eliminated. The physical basis for the method is a hypothesized periodicity correspondence between the structure within a good matching site (GMS) cluster (GMSC) and the conserved structure between dislocations. It is proposed to attribute each interfacial dislocation with a couple of correlated Burgers vectors. A set of Burgers vectors from each real lattice is identified according to the translation symmetry in a GMSC. A GMSC principle is suggested to guide the formulation of the deformation matrix A. The O-lattice theory is applied to quantify the distribution of GMSCs at the O-elements and poor matching regions at the O-cell walls. Configuration of dislocations in a general semicoherent interface is determined according to the effective O-cell wall traces in the interface. The relationship between GMS/GMSC and coincidence-site-lattice/O-lattice is elucidated for describing secondary dislocations. Several controversial issues on dislocation descriptions are discussed, including the decomposition of a net Burgers vector content, the influence of reference lattice, and the relationship between secondary dislocations and atomic steps.

Changes in the lattice constants of 55 Al-based solid solutions, as well as local lattice distortions induced by solute atoms, were studied on the basis of first-principles calculations using 3.70, 3.13, 1.56, and 0.93 at.% alloys. The first nearest-neighbor interatomic distances between the solute and the solvent Al atoms were relatively constant for all calculated Al–X systems. The calculated volume size factor and the misfit strain were in good agreement with the experimental data available in the literature. The linear relationship observed between the misfit strain and the volume size factor was explained by using the Eshelby approach. A discussion of the application of the misfit strains to the estimation of increasing yield stress due to the solid solution strengthening was also presented. The calculated extent of solid solution strengthening was in good agreement with the available experimental values.

We present first-principles calculations to study the heterojunction between a wurtzite GaN(0 0 0 1) film and a cubic Sc 2 O 3 (1 1 1) substrate. We report that the most favorable interface consists of the graphitic-like GaN nanofilms, indicating that the nanofilms can accommodate the misfit strain relaxation at heteroepitaxial interfaces. This interface structure gives rise to Ga polarity in the GaN(0 0 0 1) epitaxial film. Our findings agree with previously reported experimental results.

The temperature dependences of birefringence in thin [N(CH3)4]2Zn0.58Cu0.42Cl4 crystals in the thickness range 20 × 10−6 ≤ d ≤ 500 ↾ 10−6 m have been investigated. An increase in the temperatures of the parent phase-incommensurate phase and incommensurate phase-ferroelectric phase transitions has been found. The reasons for the shift in the phase transition temperatures with a decrease in the thickness of [N(CH3)4]2Zn0.58Cu0.42Cl4 crystal and the size effect in crystals with an incommensurate superstructure are discussed.

A phenomenological thermodynamic theory is applied to investigate the effect of misfit strain and electric field on the electrocaloric effect of P(VDF-TrFE)/SrTiO3 bilayer thin films. Theoretical results indicate that the low electric field results in the decrease of the average polarization with the increase of the relative thickness of SrTiO3 layer, and the high electric field has an opposite effect on it. Moreover, the electrocaloric effect strongly depends on the electric field. The low electric field and the small field change can lead to a maximum of the electrocaloric effect, meanwhile the high electric field or the large field change results in the opposite trend.

We investigated the effect of substrate misfit strain on the current-induced magnetization switching in magnetic tunnel junctions by combining micromagnetic simulation with phase-field microelasticity theory. Our results indicate that the positive substrate misfit strain can decrease the critical current density of magnetization switching by pushing the magnetization from out-of-plane to in-plane directions, while the negative strain pushes the magnetization back to the out-of-plane directions. The magnetic domain evolution is obtained to demonstrate the strain-assisted current-induced magnetization switching.

The age-hardenable Al–Mg–Si alloy system is strengthened by needle-shaped coherent β″ phase precipitates. Using distortion-corrected high-resolution scanning transmission electron microscopy images, we measure the considerable misfit between β″ particles and the Al matrix. The β″ phase is found to adapt its lattice parameters to the particle shape, distributing the strain in the Al matrix evenly in its cross-sectional plane. The measured misfits give a good match to reported atomistic simulations for a β″ phase with composition Mg5Al2Si4. This is a submitted manuscript of an article published by Elsevier Ltd in Scripta Materialia, 14 March 2016.

In the past decade, core/shell nanowires (NWs) have attracted much attention due to the broad variety of potential applications of these structures in future nanoelectronic and nanophotonic devices. Because of the lattice mismatch between the core and shell materials, crystal dislocations often form to relax the mismatch strains. In this article, we propose a relaxation mechanism for the misfit strains generated in the core/shell NWs, in which lattice dislocations nucleate from the outer surfaces and then propagate to the core/shell interface. An analytical model is developed to predict the critical shell thickness corresponding to defect-free core/shell NWs with respect to the growth direction.

A method based on first-principles calculations was used to construct temperature versus misfit strain phase diagrams for epitaxial (Ba x Sr 1 −x )TiO 3 ultrathin films over the entire composition range from x =0 to x =1. The predicated phase diagrams show “topologies” that are similar to those calculated by Shirokov et al. (Phy. Rev. B. 79 (2009) 144118), but with quantitative differences that are examined and explained. The dependence of the dielectric permittivity on the misfit strain and the film composition at room temperature are also investigated and compared with available theoretical predications and experimental measurements.

We present a new modification of the solid-on-solid heteroepitaxial KMC model combined with the ball and spring model allowing for efficient simulation of Stranski–Krastanov heteroepitaxial growth. The effects of intermixing are incorporated by means of a suitable prefactor to the elastic correction of the energy barrier describing the evolution of the effective misfit strain. This gives rise to a model with few parameters only which examines the surface morphology rather than the distribution of the individual elements. We support our predictions by simulations of the system InxGa1−xAs/GaAs (0 0 1) for constant temperature T = 800 K and deposition rate F = 1 ML/s. The results from simulations are in a good agreement with previous theoretical and experimental studies of heteroepitaxial systems in the literature.

A heterophase polydomain structure capable of providing large electromechanical responses was recently discovered in BiFeO 3 epitaxial ferroelectric films. In this work, the energetics of such a microstructure are analyzed to predict the equilibrium volume fraction of domains at different film–substrate lattice misfits, which is a function of the substrate lattice parameters as well as the film thickness. The results from this work provide a theoretical starting point for designing and engineering elastic polydomains in BiFeO 3 thin film materials.

This study reports the role of growth-pressure on the determination of anisotropy properties in nonpolar m-plane GaN. In the high-pressure-growth samples, unrelieved lattice misfit strain lead to larger anisotropic in-plane strains, a striated surface, lower densities of basal-plane stacking faults (BSF) and prismatic stacking faults (PSF), and a smaller anisotropic polarization. In contrast, the low-pressure-growth sample shows the opposite trend. It is suggested that the growth pressure determines the degree of relaxation of lattice misfit strain, which in turn affects the anisotropic in-plane strains, striation feature, densities of BSF and PSF, and degree of polarization. The research results can be used to optimize the growth of nonpolar m-plane GaN.

This paper presents a theoretical calculation of misfit dislocation and strain relaxation in compositionally step graded InxGa1-xN grown on GaN using the total dislocation energy at each interface. The results also compared with uniform layer of In0.17Ga0.83N and In0.14Ga0.86N grown differently on GaN. Due to having residual strain and a step increase in indium composition a lower misfit strain in upper layers and hence larger critical thickness at each interface has been reported. These effects significantly reduced the misfit dislocations from 2.6×105cm-1to 9.5×104cm-1in step graded In0.14Ga0.86N(500nm)/In0.09Ga0.91N(100nm)/In0.05Ga0.95N(100nm)/GaN layers instead of a uniform In0.14Ga0.86N(700nm)/GaN. A small residual strain of 0.0007 after 700 nm graded layer thickness has been reported with 87.04% strain relaxation.

Based on the phenomenological Landau-Devonshire theory, we investigate the effect of misfit strain on the electrocaloric effect of P(VDF-TrFE) copolymer thin films. Theoretical analysis indicates that the compressive misfit strain reduces the working temperature to a great extent where the electrocaloric effect is maximized, which is different from the result of the conventional ferroelectric thin films, such as BaTiO3. Although the compressive or tensile misfit strain does not change the maximum of the electrocaloric coefficient, the compressive misfit strain decreases the maximum of the adiabatic temperature change and the tensile misfit strain results in the opposite effect. Consequently, control of the misfit strain provides potential means to vary the working temperature for use in cooling systems.

Based on the phenomenological Landau–Devonshire theory, we investigate the film thickness dependence of ferroelectric and electro-optic properties of epitaxial BaTiO 3 thin films grown on SrTiO 3 and MgO substrates. By using the effective substrate lattice parameter concept, the film thickness dependence of misfit strain is incorporated into the theory. Therefore, the film thickness dependence of ferroelectric and electro-optic properties in epitaxial BaTiO 3 thin films can be explained. Moreover, a large quadratic electro-optic effect was obtained in the BaTiO 3 thin films, which is in good agreement with the experimental result of BaTiO 3 thin films on the MgO substrate.

The interband excitonic transition energies and their corresponding polarization properties of AlGaN and AlInN alloys pseudomorphically grown on c-plane GaN and AlN templates, have been systematically investigated under the framework of k · p perturbation theory. It is found that by changing alloy composition which is accompanied with misfit strain modulation, the valence band structure of both AlGaN and AlInN can be switched from AlN-like to GaN-like, thus leading to enhancement of the surface ultraviolet emission efficiency. Optimal alloy composition windows for efficient ultraviolet emissions have been established where AlGaN and AlInN alloys grown on AlN template show wider optimal windows than that grown on GaN template.

The microstructural evolution and the effect on in-plane magnetic properties of epitaxial Fe/MgO layers grown on InAs(001) substrates have been investigated as a function of MgO growth temperature. The Fe grows three-dimensional islands with two different in-plane textures along [010] and [110] directions on the MgO layers grown below 200 °C in remarkable contrast to two-dimensional Fe layers on the MgO layers grown above 300 °C. As the MgO growth temperature increases, both tensile-strained MgO and the subsequent Fe are simultaneously relaxed, and the distribution of 45°-rotated Fe lattices with [010] texture becomes dominant. The experimental results imply that the microstructural evolution of the Fe is strongly influenced by the underlying misfit strain within the MgO layers grown at different temperatures. The two different epitaxial relationships of the Fe islands lead to no magnetic anisotropy, while the Fe layer with the single epitaxial relationship of Fe[010]//MgO[110]//InAs[110] shows cubic m...

Interfacial dislocations are frequently observed to form during 4H-SiC epitaxy and thermal annealing. This report attempts to establish the correlation between the distribution of interfacial dislocations and the thermal stress induced by a radial temperature gradient. In addition, it is argued that they are misfit dislocations formed by the interaction between thermal strain and misfit strain.

A time-dependent phase stability diagram has been developed describing the structural evolution of TiO2 precipitates in Ti-doped sapphire (α-Al2O3). A high-pressure TiO2 phase with the α-PbO2 structure (α-TiO2) forms as a coherent precipitate in Ti-doped sapphire annealed at 1200°–1300°C; extended annealing times at these temperatures result in twinned particles, the twinning minimizing the precipitate–matrix misfit strain energy. Twinned α-TiO2 eventually transforms to the rutile structure, coincident with the loss of coherency with the sapphire matrix. Rutile nucleates directly in sapphire annealed at temperatures at 1350°C and above. Rutile is present mainly as semicoherent and twinned precipitates, the twinning occurring relatively early in the precipitation sequence.

The addition of Cr to (Mo 0.85 Nb 0.15 )Si 2 crystals significantly improves the thermal stability of the lamellar structure composed of C11 b –MoSi 2 and C40–NbSi 2 phases. Analysis using electron microscopy indicates the segregation of Cr atoms at the C40/C11 b lamellar interface. This leads to a decrease in the lattice misfit strain at the interface and better thermal stability of the lamellae.

In this paper, high-quality single crystals of (Mo0.85Nb0.15)Si2, around 8 mm in diameter and 90 mm in length, have been grown by optical heating floating zone method. Effects of chemical composition and growth rate on forming C40 structured single crystal were studied. Aligned C40/C11b lamellar structured can be formed in the as-grown crystals after post annealing at temperatures between 1473 and 1873 K. Chemical composition as well as annealing temperature are found to be two important factors to form C11b lamellae in the C40 matrix. Fully C40/C11b lamellar structure was formed after annealing at 1873 K in the present work. The aligned C40 and C11b lamellae follow a crystallographic orientation relationship of (0001)C40//(110)C11b. Dislocations were observed in some coarse C11b lamellae but never in C40 lamellae of the duplex structure. This is probably due to accumulation of misfit strain during formation of C40/C11b lamellae.

We present a theoretical investigation of the elastic interactions in a heteroepitaxial bilayer consisting of a (001) tetragonal PbZrxTi1-xO3and (001) rhombohedral PbZr1-xTixO3on a thick (001) passive substrate. Analytical expressions for the elastic interaction energies between the layers and the resultant ferroelastic twin formation have been derived as a function of the lattice misfit strain (between layers and the substrate), composition of the ferroelectric and thickness. It is found that the elastic coupling between the tetragonal and rhombohedral layers leads to the equilibrium domain fraction in the tetragonal layer several time larger than that in single-layer films of similar thickness. Most critically, the model finds a significant change in the ferroelastic domain volume fraction in the presence of an applied electric field and hence enhanced piezoelectric properties compared to single-layered epitaxial PZT thin films. Refereed/Peer-reviewed

A theoretical model is proposed for elastic stress relaxation of a buried strained cylindrical inhomogeneity, which assumes the edge misfit dislocation dipole formation in the soft matrix at some distance from the interface. The critical radius of the inhomogeneity for the formation of the edge misfit dislocation dipole is given and the influence of various parameters on the critical radius is evaluated. The result indicates that the critical radius decreases with increasing misfit strain and core radius of the misfit dislocation. It is also found that, compared to the edge misfit dislocation dipole formation in the interface, the critical radius of the inhomogeneity decreases when the location of an edge misfit dislocation dipole formation is in the soft matrix at some distance from the interface.

The critical thickness condition of the misfit dislocation formation in the system of a nanowire surrounded by a co-axial film with different elastic constants is investigated. The influence of the shear modulus ratio of the film to the nanowire (cylinder), the misfit strain and the radius of nanowire on the critical thickness of the film is discussed. The results show that the critical thickness of the film for the formation of the MDs decreases monotonically with the increment of the ratio of the shear modulus. However, if the ratio of the shear modulus is reached at a certain value, the generation of MDs is energetically favorable only when the film thickness is in some range. At last, the generation of MDs is energetically unfavorable at any value of the film thickness with the ratio of the shear modulus larger than a critical value.

The critical thickness of a film for the formation of a misfit dislocation in the system of a strained film grown on a nanopore is studied. The influence of the ratio of the shear modulus between the film and the substrate, the misfit strain and the radius of the nanopore on the critical thickness of the film is discussed. New phenomena concerning the critical thickness of the film are obtained due to the difference in elastic constants of the film and the substrate.

Current methodologies used to infer thin-film stress from curvature measurements are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to a single thin film of non-uniform thickness deposited on a substrate and subjected to the non-uniform misfit strain. Such methodologies are extended to multilayer thin films of non-uniform thickness deposited on a substrate in the present study. Each thin film may have its own non-uniform misfit strain and non-uniform thickness. We obtain the film stresses and system curvatures in terms of the misfit strains and thickness in thin films. We derive the film stresses and interface shear stresses in terms of system curvatures and film thicknesses. They all feature a "non-local" dependence on curvatures, which make full-field measurement a necessity for the experimental inference of such stresses.

Under certain growth conditions for systems with a film/substrate lattice misfit, the deposited material is known to aggregate into island-like shapes. We have obtained an analytical expression of the total free energy, which consists of strain energy, surface energy and interfacial energy of a coherent island/substrate system, and the change of equilibrium aspect ratio versus the volume of the island and the misfit of lattices in the system, which provides a broad perspective on island behaviour. These then were used to study the equilibrium shapes of the system. The results show that in order to minimize the total free energy, a coherent island will have a particular height-to-width aspect ratio, called equilibrium aspect ratio, that is a function of the island volume and misfit. The aspect ratio is increased with increasing island volume at a fixed misfit, and with increasing misfit strain between the island and substrate at a fixed island volume. Moreover, the effect of misfit dislocation on the equilibrium shape of the island is also examined. The results obtained are in good agreement with experiment of observations and thus can serve as a basis for interpreting the experiments.

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 BaTiO$_3$, 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., Comment: 14 pages, submitted to Phase Transitions

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 Widmanstatten θ ′ precipitates of two different thicknesses (1.2 and 2.0 nm) are compared. It is shown experimentally that the thinner precipitates grow more slowly than their 2.0 nm 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.

We investigate the polarization and dielectric properties of ferroelectric BaTiO3 thin film grown compositionally graded substrate by using first-principles method. Due to the spatial variation of the misfit strain between film and substrate, the polarization in the film decreases gradually along x direction of the film. Moreover, localization of the polarization also results in large spatial variation of the dielectric constant in the ferroelectric thin film. Our results suggest that such interesting properties of ferroelectric thin films can be controlled by choosing appropriate compositionally graded substrates.

The precipitation processes from G.P. zones to γ’ in a Cu−0.9wt%Be alloy single crystal containing only the G.P. zones parallel to the matrix (001)α plane are investigated by high-resolution electron microscopy. The precipitate phases follow a G.P. zone → γ” → γI + γ’ sequence. The G.P. zone to γI phase transformation occurs successively via γ” during aging, while the γ’ phase heterogeneously precipitates on the γI phase. From length-change measurements during aging, the misfit strains of γ’ precipitates in directions perpendicular and parallel to [001]α are estimated as ε11 =ε22 = −0.03 and ε33 = −0.09, respectively. The observation that the estimated absolute value of ε33 is much smaller than that of ε33 = −0.25 calculated using lattice parameters of the γ’ phase and Cu matrix is understood in terms of the relaxation of ε33 by interfacial misfit dislocations.

We investigated the contribution to the high yield strength due to the solid solution strengthening in nanocrystalline Al-Ti alloys produced by a vapor quench method. The misfit strain due to solute Ti atom in aluminum was obtained from the first principles calculation. Then, the theoretical result of the contribution to the yield strength due to the solid solution strengthening was estimated from the misfit strain using the Friedel’s theory. In dilute Al-Ti alloy, the theoretical results of the solid solution strengthening from the misfit strain was in good agreement with the analytical result using the measured grain size and yield stress.

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis and co-workers [Huang, Y., Ngo, D., Rosakis, A.J., 2005. Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures. Acta Mech. Sin. 21, 362–370; Huang, Y., Rosakis A.J., 2005. Extension of Stoney’s Formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry. J. Mech. Phys. Solids 53, 2483–2500; Ngo, D., Huang, Y., Rosakis, A. J., Feng, X. 2006. Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between non-uniform film stresses and system curvatures. Thin Solid Films (in press)] established methods for film/substrate system subject to non-uniform misfit strain and temperature changes. The film stresses were found to depend non-locally on system curvatures (i.e., depend on the full-field curvatures). The existing methods, however, all assume uniform film thickness which is often violated in the thin film/substrate system. We extend these methods to arbitrarily non-uniform film thickness for the thin film/substrate system subject to non-uniform misfit strain. Remarkably the stress-curvature relation for uniform film thickness still holds if the film thickness is replaced by its local value at the point where the stress is evaluated. This result has been experimentally validated in Part II of this paper.