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The elastically driven, self-assembled polydomain nanostructures (elastic domains) in ferroelectric films are both scientifically intriguing and practically important, since the interfaces and long-range elastic and electric fields associated with the periodic nanoscale modulation in structure can endow unique and desirable physical properties to the ferroelectric films, including large piezoelectric and dielectric responses, enhanced pyroelectric, and electrocaloric performances, as well as electro-optical effects (anomalous photovoltaic effect, for example). In this chapter, thermodynamics of the formation of elastic domains in epitaxial ferroelectric films is presented, together with a focused review on the theoretical and experimental studies. In addition, methods of domain engineering aimed at achieving an optimal polydomain structure for certain energy applications are discussed.

A review of theoretical models, phase field modeling and experimental studies of domain structures in epitaxial films is presented. The thermodynamic theory of such domain structures is presented within the macroscopic thermo-mechanical framework. The theory allows for the evaluation of the main parameters of the domain structure using the energy minimization approach applied to the energy of elastic interactions. For homophase (polytwin) films, the thermodynamic theory provides a quantitative tool that can be used to estimate domain fractions in the film and the type of domain structure architecture. For heterophase films, the theory describes (a) the conditions under which two-phase structures can be obtained in epitaxial films, and (b) the phase and domain fractions in these films. The thermodynamic theory can also be used to describe the extrinsic contributions from domain structures to the functional properties of epitaxial ferroelectric films. The review of phase field modeling demonstrates that computational results reproduce the predictions of the thermodynamic theory. It is also shown that the phase field modeling that utilizes the energy minimization procedure for elastic and interfacial energies can be used to predict domain morphology for the films with two-phase structures produced either by phase transformation or through the co-deposition of immiscible phases. The experimental data presented in the review validate predictions of the thermodynamic model and the results of phase field modeling.

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.

In this work, the thermodynamics of formation of tetragonal and rhombohedral heterophase polydomains in ferroelectric films is explained by the theory of elastic domains. The energetics of the heterophase polydomain microstructure are analyzed. The three major energy terms determining the crystalline orientation of the interdomain interface, i.e. interdomain elastic energy, interdomain electrostatic energy and domain interface energy, are investigated and compared. The crystalline orientation of the elastically best fitting plane between the two phases is analytically solved under an isotropic approximation of elasticity. It is found that a {1 1 2} type of domain interface minimizes interdomain elastic energies. Using available material parameters, it is found that the {1 1 2} domain interface prevails in Pb(Zr, Ti)O3, Pb(Mg1/3 Nb2/3)O3–PbTiO3 and BiFeO3 heterophase polydomains under zero applied electric field, as elastic energy is the dominant factor of interdomain interactions in all three systems. On the other hand, an increasing interdomain electrostatic energy under a poling field may induce a different domain interface, which is beneficial to extrinsic electromechanical responses.

The model of the P(E) hysteresis in dielectric—ferroelectric bilayers and weak—strong ferroelectric bilayers is presented with the phase field modeling of the domain structure and P(E) curves in the compositionally graded m BaxSr (1-x) TiO 3 – n BaTiO 3 bilayers on SrTiO 3 substrate. It is shown that the hysteresis loop depends on the film composition and structure and varies from simple rectangular to complex. The coercive field and the single-domain to polydomain transition depend on the film composition and structure. There is a significant difference between the behavior of through thickness domain structures and columnar domain structures localized in one layer.

The domain structure and dielectric properties in multilayered compositionally graded BaxSr 1-x TiO 3 films on SrTiO 3 substrates are studied using phase field modeling with a uniaxial ferroelectri...

This study investigates the spinodal mechanism of domain formation and switching through the loss of stability of a single-domain (SD) state with respect to a polydomain (PD) state in thin ferroelectric films with dead layers. The macroscopic thermodynamic model of a homogenized domain structure (DS) is used to analyze the depolarizing field effect on the transitions between SD and PD states and the shape of the P(E) hysteresis loop. Phase field modeling is used to study the inhomogeneities and film thickness effects on DS and P(E) hysteresis. Such modeling of relatively thick films produces P(E) hysteresis loops of a shape similar to that predicted by the macroscopic model. The results of the analysis demonstrate that the SD → PD transition can proceed by the spinodal mechanism in thin films, while the nucleation and growth mechanism should operate in thick films. It is shown that columnar and stripe DS can be produced in thin films.

A thermodynamic analysis of graded ferroelectric films demonstrates that in the equilibrium state the films are subdivided into a single-domain band and a polydomain band which consists of wedge-shape domains. Polarization under an external electrostatic field proceeds through an inter-band boundary movement due to growth or shrinkage of the wedge domains. It is shown how the domain structure and evolution are determined by the principal characteristics of the film: the distribution of the spontaneous polarization and dielectric constant. Graded films exhibit a sharp increase of polarization with the field for weak fields, with a drop of the dielectric constant when the field is increasing. A general approach to finding the dependence of the displacement and the wedge-domain shape on the field as well as analytical solutions for the p{sup 4} Landau-Devonshire and parabolic potentials are presented.

Ni47Ti53 films of varying thickness were deposited onto Ni56Ti44 substrates. Annealing the films produced compositional gradients through diffusion modification. Nanoindentation measurements were used to probe the mechanical properties at various depths into the film. The films exhibited a variation in elastic modulus as a function of indentation depth that depended on the thickness of the film. A self-similarity principle permitted the mechanical properties of the graded NiTi films to be resolved further into substrate, beyond the contact depth of the tip. The observed variation of elastic modulus with indentation depth in the graded NiTi films was considered to be a combined response from changes in microstructure, substrate effects, and mechanically-induced phase transformations. This variation was predicted using an analysis that accounted for the transformation effects occurring under the tip during loading and the graded distribution of martensite volume fraction obtained from diffusion modification.

Substrate clamping and inter-domain pinning limit movement of non-180° domain walls in ferroelectric epitaxial films thereby reducing the resulting piezoelectric response of ferroelectric layers. Our theoretical calculations and experimental studies of the epitaxial PbZrxTi1–xO3 films grown on single crystal SrTiO3 demonstrate that for film compositions near the morphotropic phase boundary it is possible to obtain mobile two-domain architectures by selecting the appropriate substrate orientation. Transmission electron microscopy, X-ray diffraction analysis, and piezoelectric force microscopy revealed that the PbZr0.52Ti0.48O3 films grown on (101) SrTiO3 substrates feature self-assembled two-domain structures, consisting of two tetragonal domain variants. For these films, the low-field piezoelectric coefficient measured in the direction normal to the film surface (d33) is 200 pm V–1, which agrees well with the theoretical predictions. Under external AC electric fields of about 30 kV cm–1, the (101) films exhibit reversible longitudinal strains as high as 0.35 %, which correspond to the effective piezoelectric coefficients in the order of 1000 pm V–1 and can be explained by elastic softening of the PbZrxTi1–xO3 ferroelectrics near the morphotropic phase boundary.

A thermodynamic approach was used to describe the formation and magnetoelectric response of composite multiferroic films. Experimental and theoretical results that address the origins of different phase morphologies in epitaxial spinel-perovskite nanostructures grown on differently oriented substrates are presented. A theoretical model of magnetoelectric coupling in multiferroic nanostructures that considers a microscopic mechanism of magnetization in single-domain magnetic nanorods is described. This model explains a discontinuous electromagnetic coupling, as observed experimentally, and predicts a hysteretic behavior of magnetization under external electric fields.

Metal–hydride phase transformations in solids commonly proceed with hysteresis. The extrinsic component of hysteresis is the result of the dissipation of energy of internal stress due to plastic deformation and fracture. It can be mitigated on the nanoscale, where plastic deformation and fracture are suppressed and the transformation proceeds through formation and evolution of coherent phases. However, the phase coherency introduces intrinsic thermodynamic hysteresis, preventing reversible transformation. In this paper, it is shown that thermodynamic hysteresis of coherent metal–hydride transformation can be eliminated in epitaxial film due to substrate constraint. Film–substrate interaction leads to formation of heterophase polydomain nanostructure with variable phase fraction which can change reversibly by varying temperature in a closed system or chemical potential in an open system.

The formation and electro-magnetic coupling of self-assembling nanostructures consisting of ferrimagnetic rods embedded in a ferroelectric matrix have been analyzed using a thermodynamic approach. The resulting nanostructure architectures are determined by minimizing the free energy including the elastic energy associated with the epitaxial stresses, which arise during the growth of nanosize constituent phases. The magnetic response to the external electric field has been studied by minimization of the Landau-type free energy for ferrimagnetic and ferroelectric phases with elastic interactions between them. It has been shown that depending on the mechanism of rotation of magnetic moments in single-domain nano-rods the external electric field induces a continuous or discontinuous change of magnetization. The formation of a CoFe2O4--PbTiO3 nanostructure grown on SrTiO3 substrate and its response to an electric field is considered as an example.

Ferroelectric multilayers and superlattices have gained interest for dynamic random access memory (DRAM) applications and as active elements in tunable microwave devices in the telecommunications industry. A number of experimental studies have shown that these materials have many peculiar properties which cannot be described by a simple series connection of the individual layers that make up the heterostructures. A thermodynamic analysis is presented to demonstrate that ferroelectric multilayers interact through internal elastic, electrical, and electromechanical fields and the strength of the coupling can be quantitatively described using Landau theory of phase transformations, theory of elasticity, and principles of electrostatics. The theoretical analysis shows that compositional variations across ferroelectric bilayers result in a broken spatial inversion symmetry that can lead to asymmetric thermodynamic potentials favoring one ferroelectric ground state over the other. Furthermore, the thermodynamic modeling indicates that there is a strong electrostatic coupling between the layers that leads to the suppression of ferroelectricity at a critical paraelectric layer thickness for ferroelectric-paraelectric bilayers. This bilayer is expected to have a gigantic dielectric response similar to the dielectric anomaly near Curie-Weiss temperature in homogeneous ferroelectrics at this critical thickness.

The coexistence of tetragonal and rhombohedral phases as elastic domains is studied in this paper for lead zirconate titanate (PZT) ferroelectric films near the morphotropic phase boundary (MPB). The volume fractions of the phases and different twin components are obtained as functions of misfit strain and film orientation. It is shown that the superior electromechanical properties of MPB-PZT films may be understood on the basis of a field-induced evolution of the heterophase polydomain structure.

The orientation dependences of the converse longitudinal piezoelectric constant d33,f, and the in-plane converse piezoelectric constant e31,f, are calculated for tetragonal barium titanate epitaxial films. The calculations demonstrate that both e31,f and d33,f have their maximum values along an axis close to the (1 1 1) direction of the pseudo-cubic system, which are similar to the orientation dependence results for a tetragonal BaTiO3 single crystal. The calculated piezoelectric constants for a (1 1 1) oriented BaTiO3 epitaxial film (e31,f = −23 C/m2, d33,f = 124 pm/V) suggest that it is a good candidate material for lead-free MEMS applications.

Due to substrate clamping, the effective piezoelectric coefficients of an epitaxial ferroelectric film are usually different from those of bulk materials. The modifications of intrinsic piezoelectric responses by film–substrate in-plane stresses are quantitatively illustrated for a ferroelectric film with arbitrary orientation and structure. Consequently, the intrinsic effective piezoelectric coefficients of an epitaxial ferroelectric film are generally formulated.

We present a thermodynamic analysis and phase field modeling of self-assembled multiphase nanostructures produced by phase transformations in constrained layers. Due to coherency between the phases, the elastic interactions between them and between each phase and the substrate layer play an important role in the formation of the nanostructures. It has been shown that a variety of morphologies of heterophase nanostructures can be obtained depending on the crystallographic characteristics of transformations, elastic properties of the phases, relative fractions of the phases, and the thickness of the film. The results obtained by phase-field modeling agree well with predictions of an analytical thermodynamic model. The final equilibrium structures are determined by thermodynamic parameters and do not depend on the transformation path and, therefore, the phase-field approach developed in this paper can be expanded to finding equilibrium multiphase coherent nanostructures created as a result of solid-solid or solid-liquid transformations as well as during co-deposition on a substrate.

The general orientation dependence of the intrinsic converse longitudinal piezoelectric constant dnnf in an epitaxial rhombohedral film is calculated by taking into account the effect of substrate clamping. Theoretical predictions are made for dnnf of epitaxial 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 rhombohedral films, which are compared with experimental results on pseudo-cubic (001), (110) and (111) orientations.

The converse piezoelectric response of a thin film constrained by a substrate is analyzed in different geometries under various boundary conditions. We considerthe effects of elastic deformation of the substrate on the total displacement of thefilm surface induced by the electric field. The change of film thickness and the bending curvature of a film/substrate couple are calculated. For a thin film island clamped on a large thick substrate, the theoretical estimation of the piezoresponse, including a local bending in the vicinity of the island/substrate interface, is in agreement with the finite element calculation.

The theoretical analysis and phase-field modeling of elastic domain structures in constrained layers depending on their misfit and thickness are presented. Domain diagrams that demonstrate how different domain structures can be obtained by manipulating parameters of constraints are constructed for a model system with cubic-tetragonal transformation. It is shown that depending on the misfit, three-domain stress-free structures (hierarchical and cellular) and two-domain uniaxially stressed structures are the equilibrium states for relatively thick films. When the film thickness decreases, the area of a three-domain hierarchical structure shrinks and disappears followed by the disappearing cellular domain structures. In thin films, two-domain structures with asymmetric architectures are stable at negative symmetric misfit (in-plane contraction), while two-domain structures with symmetric domain architectures are stable at positive symmetric misfit (in-plane expansion). The results of the phase-field modeling are discussed in connection with the experimental data available for film/substrate ferroelectric heterostructures.

The evolution of martensitic microstructure and stress in a constrained film coupled with a substrate under cooling and heating is considered. Thermodynamic analysis has done using the special phase diagrams constructed in coordinates temperature-film/ substrate misfit.

Upon substrate removal nano-crystalline cubic BaTiO3 thin films transformed into the tetragonal phase. Randomly oriented nano-crystalline BaTiO3 films were prepared with moderate residual tensile stress by sol-gel processing or RF sputtering. The low dielectric constant (110 ± 20) and the X-ray diffraction spectra identified the films as being cubic at room temperature. Despite the tensile stress in the substrate-supported films, the free-standing films became corrugated, indicating 0.3–0.5% lateral expansion. The fact that the cubic-to-tetragonal phase transition was responsible for the lateral expansion has been confirmed by a fivefold increase of the dielectric constant (620 ± 10) and a detectable piezoelectric effect.

The phase transformation in a constrained layer is the subject of this article. The formation and evolution of polydomain microstructure under external stress in the constrained layer are investigated by phase-field simulation and analytically using homogeneous approximation. As a result of simulation, it has been shown that the three-domain hierarchical structure can be formed in the epitaxial films. Under external stress there are two types of morphological transitions: from the three-domain structure to the two-domain one and from the hierarchical three-domain structure to the cellular three-domain structure. The results of phase-field simulation are compared with conclusions of homogenous theory and with available experimental data.

The theory of coherent phase diagrams is expanded to phase transformations in films. The misfit between the phases dictates their layer arrangement with an interface parallel to film surfaces. Then, the transformational self-strain leads to the film bending. The phase equilibrium analysis shows that the polymorphic transformation in a single component system proceeds with the thermodynamic hysteresis. However, the reversible change of the two-phase equilibrium with temperature is possible, if the phase fractions are maintained within a range (1/2, 2/3). The character of polymorphic phase transformations in a binary system depends on the concentration of a second component. The quasi-single component transformation takes place at small concentrations. The reversible coherent phase transformation should be observed at the concentration larger than the critical one. The irreversible transformations take place at intermediate concentrations. The irreversible transformations begin with the formation of a finite fraction of the second phase. Then, the two-phase system evaluates with temperature to the final two-phase state that transfers discontinuously to a single-phase state. The concentration diagram does not coincide with the phase diagram. The concentrations in the transforming phases change non-monotonously with temperature.

The uniaxial stress field in shape memory alloy (SMA) films patterned into thin strips increases the transformation induced deflection of SMA/Si cantilever bimorphs in comparison to cantilevers with planar films. In the single phase temperature ranges T>Af, Ms and T

The superelastic deformation of an adaptive layer composite containing a shape memory alloy as an active component is considered in this paper. It is shown that the intrinsic instability of superelastic deformation can be suppressed in such kind of composite. The stability analysis of superelastic deformation allows one to formulate design principles of adaptive composites with controlled stress-strain hysteresis. The analysis of composite with sufficiently different elastic moduli of passive and active layers is a necessary step for using adaptive composites in applications which require a large reversible superelastic deformation.

Understanding the relationship between the uptake of hydrogen gas and hydride phase formation and evolution in metal solids is a phenomenon of significant technological importance due to current development of hydrogen storage devices, sensors, and membranes. The performance of these devices is degraded by structural defect formation during incoherent metal-hydride phase transformation. In this work, atomic force and scanning electron microscopy reveal formation of nanoplates along the ⟨111⟩ directions in a (111) epitaxial Pd film. These nanostructures are observed after high temperature and high pressure gas phase hydrogenation and cooling in ambient temperature. Transmission electron microsocpy (TEM) analysis of a posthydrogenated film did not show considerable plastic deformation. The size of the nanoplates increased with increasing Pd film thickness. A formation mechanism of nanoplates is proposed: cooling the sample reactor in ambient temperature after hydrogen loading induced formation of coherent or partially coherent β-phase plates along {100} planes corresponding to minimum elastic energy of interaction between metal and hydride phases.

Deformation as a result of solid–solid phase transformations, particularly martensitic, is the subject of this paper. The thermodynamic theory of elastic domains is applied to a transformation with a polytwin product phase which consists of two or more different domains (twins) forming plane–parallel alternations. The volume fractions of the phases and different twin components in the product phase are obtained as functions of applied stress (strain) and temperature. It is shown that during stress- or strain-induced transformation a twin fraction in martensite plates changes and a product phase becomes incompatible with an initial phase. This fact leads to the intrinsic instability of a transformational deformation, which appears as a negative Young's modulus under strain-controlled deformation and a thermodynamic hysteresis under stress-controlled deformation. The deformation is irreversible also due to microstructure irreversibility of the transformation from a polytwin state to a single-domain state. Superelastic deformation due to martensitic transformations is discussed as an application of the presented theory.

Epitaxial ferroelectric films undergoing a cubic-tetragonal phase transformation relax internal stresses due to the structural phase transformation and the difference in the thermal expansion coefficients of the film and the substrate by forming polydomain structures. The most commonly observed polydomain structure is the c/a/c/a polytwin which only partially relieves the internal stresses. Relatively thicker films may completely reduce internal stresses if all three variants of the ferroelectric phase are brought together such that the film has the same in-plane size as the substrate. In this article, we provide experimental evidence on the formation of the three-domain structure based on transmission electron microscopy in 450 nm thick (001) PbZr0.2Ti0.8O3 films on (001) SrTiO3 grown by pulsed laser deposition. X-ray diffraction studies show that the film is fully relaxed. Experimental data is analyzed in terms of a domain stability map. It is shown that the observed structure in epitaxial ferroelectric...

A high resolution magneto-optical technique with a magnetic indicator film was used to study the effect of a regular array of micrometer-sized mechanical indentations on magnetization dynamics at the surface of a twinned single crystal of YBa2Cu3O7−δ as a function of applied magnetic field, Ha (0 to ±68 mT) at temperatures in the range of 10–70 K. Direct visualization of the magnetic flux interaction with the individual indentations was observed for the first time. During magnetization at low Ha up to 15 mT at 60 K, the first row of indentations provides resistance to the flux front. In the indented area, flux is preferably pinned at the indentation sites. With increasing Ha, the vortex density at the indentations approaches the magnetic flux density in the surrounding material. During demagnetization down to Ha=0 mT, the outgoing flux is trapped by the indentations in areas where the density of the trapped flux is small; flux is also trapped along the (110) twin boundaries behind the indentations. For Ha...

Thin films of composition (Ba,Sr)yTiO2+y with 0.43 ≤ y ≤; 1.64, were deposited by metalorganic chemical vapor deposition on (100) MgO substrates at various growth conditions. X-ray diffraction and transmission electron microscopy studies showed that the films were composed of epitaxial Ba1–xSrxTiO3 (x ≈0.06) grains and an amorphous phase. The orientation of the tetragonal Ba1–xSrxTiO3 grains (pure a axis, pure c axis, or a mix of the two) was found to be strongly dependent upon film composition. This composition dependence is explained for the majority of the Ti-rich films by an analysis of average strains in the two-phase films, assuming a compressive strain of ≈1% in the amorphous phase.

A new class of materials, layer composites containing adaptive polydomain components, is considered. Polydomain structures can be the result of constrained phase transformation. Polydomain structures consist of periodically alternating layers of different stable and metastable phases (heterophase polydomain) or differently oriented domains of product phase (e.g. polytwin). The domain interface movement enables an additional mode of deformation. The theory predicts unusual physical and mechanical properties of composites, particularly, considerable decrease of the effective elastic moduli of composites, nonlinear stress–strain relations, and critical behavior at small thickness of an active layer.

Deformation of an adaptive heterophase crystal with variable microstructure is considered. Under mechanical constraint the phase transformation in single component systems result in an equilibrium two-phase mixture. A typical equilibrium microstructure of a constrained crystal is a polydomain, i.e. an alternation of the plane-parallel layers, or domains, of the parent and product phases with a special crystallographic orientation of interfaces between domains. The relative fractions of the domains are determined by the external conditions. The free energy of a polydomain is a non-convex function of constrained strain. Therefore, the stress–strain relation at displacement controlled deformation of the polydomain is characterized by a negative Young’s modulus. If deformation proceeds under stress control, a hysteretic stress–strain curve on loading and unloading should be observed instead of a negative stress–strain slope. Besides this thermodynamic hysteresis, anelastic hysteresis appears at a constant strain-rate deformation, if the microstructure relaxes more slowly than the strain changes.

We have studied the effect of misfit strain on the microstructure and properties of ferroelectric lead zirconate titanate thin films. We have changed the misfit strain by varying the film thickness and studied the thickness effect on the domain formation of epitaxial PbZr0.2Ti0.8O3 (PZT) films grown by pulsed laser deposition on (001) LaAlO3 substrates with La0.5Sr0.5CoO3 (LSCO) electrodes. The nominal thickness of the PZT films was varied from 60 to 400 nm with the LSCO electrode thickness kept constant at 50 nm. X-ray diffraction experiments show that the films relax via the formation of a domains, the fraction of which increase with the ferroelectric film thickness. The c-axis lattice constant of PZT films calculated from the 002 reflection decreases with increasing film thickness and approaches the bulk value of ∼0.413 nm in the films thicker than 300 nm. Cross-sectional transmission electron microscopy images reveal that the a-domain fraction and period increase with increasing film thickness. The relaxation of misfit strain in the film is accompanied by systematic changes in the polarization properties, as well as the switching fields, quantified by the coercive field and the activation field.

Deformation of polydomain crystalline materials consisting of domains of different phases or domains of differently oriented areas of the same phase are considered. These polydomain materials are adaptive if their domain microstructure can change in response to a change of external mechanical or electrical fields. For ferroelastic and martensitic transformations in shape memory alloys the domain interfaces are so mobile that the deformation is almost reversible. Therefore, it can be treated as a superelastic deformation which is additional to the elastic one. Thermodynamic analysis of the evolution of an equilibrium microstructure has shown that the mechanical behavior of a transforming crystal is in principle different for displacement controlled deformation and for load controlled deformation. The different types of the microstructure are considered: (1) a heterophase polydomain: (2) a heterostructures containing besides an adaptive component, a passive component which remains unchangeable duri...

The effect of uniaxial external stress fields applied during the cooling down from the deposition temperature on the domain structure of epitaxial ferroelectric or ferroelastic films is investigated using the domain stability map. This map predicts stable domain structures and is constructed in the coordinates of the misfit strain between the cubic substrate and the film, and the tetragonality of the film. It is shown that with the application of a stress field perpendicular to the film-substrate interface, perfectly c-axis oriented films may be obtained.

Polydomain micro- and nano-structures are natural products of phase transformations in solids. The trend to minimize the energy of internal long-range fields (magnetic, electric or mechanical) leads to the formation of the arrangement of domains of different phases or differently oriented domains of the same phase [1–3]. Transformations of bulk materials usually result in formation of complex irregular polydomain structures, which are difficult to control. However, the advance of thin film technology makes it possible to obtain well- controlled polydomain structures with desirable properties. The objective of this paper is to show how controlled structures of elastic domain in constrained single crystalline layers are developed and how these structures can be designed by engineering of a constraint.

A map showing regions of stability of possible domain structures and relative fractions of domains in a polytwin structure is developed for epitaxial heterostructures with active layers which undergo a cubic–tetragonal or a tetragonal–orthorhombic transformation. This map, which is also applicable to epitaxial film–substrate systems, shows the dependence of the polytwin structure on misfit strain, lattice parameters of the product phase, and mechanical stress. A uniaxial stress field applied during cooling down from the growth temperature strongly affects the domain structure selection and perfect single-domain structures may be obtained with such fields. For polytwin layers with thicknesses close to the critical thickness for domain formation, microstresses must be taken into consideration and the domain stability map is modified accordingly. Misfit dislocation generation at the deposition temperature is taken into account through a temperature dependent effective substrate lattice parameter. As examples...

Thermodynamics of a coherent phase transformation in a constrained solid is analyzed. Under mechanical constraint the phase transformations in single component systems result in an equilibrium two-phase mixture. A typical equilibrium two-phase microstructure of the initial-product phase mixture is an alternation of the plane-parallel layers of the phases with a special crystallographic orientation of interfaces between layers. The relative fractions of the phases are determined by the external conditions. The two-phase free energy is a non-convex function of constrained strain. Therefore, the stress-strain relation at displacement controlled deformation of the transforming two-phase mixture is characterized by a negative Young's modulus. If deformation proceeds under stress control, a hysteretic stress-strain curve on loading and unloading should be observed instead of a negative stress-strain slope.

Thermodynamics of the formation of the coherent phase in the crystal under uniform stress is considered. The self-strain of transformation is a source of internal stresses in the coherent heterophase system. Due to the elastic energy of internal stresses the T - σ line of the phase equilibrium is split into two transformation lines. The transformation is possible only beyond these lines, where a metastable phase becomes unstable with respect to the macroscopic volume of a stable phase. In the paper the positions of the transformation lines are calculated for polymorphic phase transformation. These lines determine the thermodynamic hysteresis of direct and reverse transformations during cooling-heating or under the stress.

Metal hydrides present a feasible means of energy storage and hydrogen sensing but have several performance criteria that must be addressed, including the hysteresis effect during hydrogen loading and unloading. We present the results of a theoretical and experimental study which demonstrates the possibility to control or eliminate hysteresis during metal-hydride transformation in epitaxial Pd thin films. Theoretical analysis predicts stabilization of two-phase metal-hydride state in film due to its elastic interaction with the substrate. It is shown, by atomic force and scanning electron microscopy, that transformation in 100nm thick epitaxial Pd films on Al2O3 substrate proceeds by the formation of transversely modulated two-phase nanostructure. Morphology and crystallographic orientation of the metal-hydride interface corresponds to the theoretically predicted characteristics of coherent phases.

Mechanically synthesized, reproducible polytwins of an In-22.5 at. pct Tl shape memory alloy were studied quantitatively for their deformation behavior due to bending stresses, in the ferroelastic and rubberlike temperature regime, within situ video recordings of the evolving mesostructure. The experimental ratios of the twin modulus, ET, to the elastic modulus, Eel, were two orders of magnitude higher than the theoretically calculated values. Further investigations to reconcile this discrepancy revealed a fine substructure within each domain of the polytwin. The response coefficient of this substructure, rather than the elastic modulus, was found to be the controlling deformation parameter for the polytwin. Theoretically predicted results were modified, which established a close agreement with the experimental results.