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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.

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...

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.

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...

The thermodynamic effects of microstresses on the formation of polydomain heterostructures are considered. The microstresses arise due to the periodic deviation of the actual misfit from the average misfit on the interfaces between a polydomain layer and neighboring layers. The thermodynamic analysis is restricted to heterostructures with D/h

The orientation dependence of the converse piezoelectric constants in epitaxial single domain piezoelectric films constrained by substrate is calculated. The calculations are supported by the experimental measuring results of longitudinal piezoelectric constants of ferroelectric tetragonal Pb(Zr0.2Ti0.8)O3 thin films with (001), (011), and (111) orientations.

Patterning thin ferroelectric films into discrete islands is an effective way to release the constraint imposed by a substrate and the unpoled nonpiezoactive surrounding film to enhance the film piezoresponse. The converse piezoresponse measured by the surface displacement of ferroelectric islands, with lateral size changing from a nanoscale to a continuous film, has been modeled using three-dimensional finite element method. The modeling has shown that piezodeformation of the islands results in a local deformation of a substrate in the vicinity of island. The deformation is larger when the substrate is softer. The deformation, together with clamping strain in the film, decreases the effective d33 of the film island. The effect of the top electrode on d33 measured by surface displacement is also modeled. The piezoresponse of different size island capacitors with PbZr0.5Ti0.5O3/SrTiO3/Si and PbZr0.2Ti0.8O3/SrTiO3 heterostructures has been calculated. The results of modeling are in good agreement with experimental data on d33 obtained by piezoresponse force microscopy.

90° elastic domains were observed after local polings in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 thin films via piezoresponse force microscopy. An area of internal stress arises under a conductive atomic force microscope tip due to the opposite signs of the converse piezoelectric effects in the switched domain and the unswitched films surrounding. The formation of 90° domains leads to the relaxation of the internal stress and stabilization of 180° domain after turning off the electric field applied by the tip. The criterion that formulates the necessary condition for realization of the relaxation mechanism is presented as well.

A crystal which can be in two possible phase states is considered. During tensile extension the crystal is deformed elastically. After a certain amount of elastic strain a phase transformation begins. For each fixed level of strain an equilibrium mesostructure is established, which corresponds to a minimum in the free energy of the crystal. The equilibrium mesostructure consists of plane, parallel layers of a product phase separated by layers of an initial phase. The product phase itself consists of two or more different domains (twins) forming plane, parallel alternations. The volume fractions of the phases and of different twin components in the product phase are functions of strain and temperature. Above a critical temperature the product phase is a single domain (untwinned). The stress‐strain curve which reflects the evolution of the equilibrium mesostructure is calculated. For deformation under a strain control the calculated equilibrium stress‐strain curve has a section with negative slope that corr...

We report on the out-of-plane piezoelectric response (d33), measured via piezoresponse scanning force microscopy, of submicron capacitors fabricated from epitaxial PbZrxTi1−xO3 thin films. Investigations on 1 μm2 and smaller capacitors show that the substrate-induced constraint is dramatically reduced by nanostructuring. At zero field, the experimentally measured values of d33 for clamped as well as submicron capacitors are in good agreement with the predictions from thermodynamic theory. The theory also describes very well the field dependence of the piezoresponse of clamped capacitors of key compositions on the tetragonal side of the PbZrxTi1−xO3 phase diagram as well as the behavior of submicron PbZr0.2Ti0.8O3 (hard ferroelectric) capacitors. However, the field-dependent piezoresponse of submicron capacitors in compositions closer to the morphotropic phase boundary (soft ferroelectrics) is different from the behavior predicted by the theoretical calculations.

We have investigated the polydomain formation in 100–200-nm-thick PbZr0.2Ti0.8O3 epitaxial thin films on vicinally cut (100) oriented SrTiO3 substrates. Our results show that there is a preferential location of the nucleation of the a domains along the step edges of the underlying substrate. By piezo-response microscopy, we show that all a domains have their polarization aligned along the same direction. This result is in contrast to flat substrates where fourfold symmetry of a domains is observed. We observe that the critical thickness for a domain formation is much lower than that for PbZr0.2Ti0.8O3 films grown on flat substrates. We have developed a model based on minimization of elastic energy to describe the effect of localized stresses at step edges on the formation of a domains in the ferroelectric layer.

A series of heteroepitaxial BaxSr1−xTiO3 thin films with composition x=0.50 were deposited on (001) MgO substrates by pulsed-laser deposition. The thickness of the films was varied from 14 to 500 nm to produce a systematically decreasing level of in-plane tensile stresses. The microstructural and crystallographic features of the films were determined via transmission electron microscopy and x-ray diffraction. A theoretical treatment of the in-plane misfit strain as a function of film thickness is in agreement with the measured out-of-plane lattice parameters. Electrical measurements indicate a drop in the dielectric constant from 2350 for highly stressed thin films to 1700 for relaxed thicker films. The variation in the dielectric constant with the misfit strain is in accordance with a thermodynamic model developed. The relationship between the dielectric constant and electric field is also described by extending the thermodynamic model and taking the effect of electric field into account. A new definitio...

The time-dependent relaxation of the remanent polarization in epitaxial lead zirconate titanate (PbZr0.2Ti0.8O3) ferroelectric thin films, containing a uniform two-dimensional grid of 90° domains (c axis in the plane of the film), is examined using piezoresponse microscopy. The 90° domain walls preferentially nucleate the 180° reverse domains during relaxation, with a significant directional anisotropy. Relaxation occurs through the nucleation and growth of reverse domains, which subsequently coalesce and consume the entire region as a function of time.

A series of heteroepitaxial Ba0.6Sr0.4TiO3 were grown on 0.29(LaAlO3):0.35(Sr2TaAlO6) substrates using pulsed-laser deposition. X-ray characterization revealed compressive in-plane stresses in the thinnest films, which were relaxed in a continuous fashion with increasing thickness. A theoretical treatment of the misfit strain was in good agreement with the measured out-of-plane lattice parameter. The low-frequency dielectric constant was measured to be significantly less than the bulk value and found to decrease rapidly for films less than 100 nm. A thermodynamic model was developed to understand the reduction in dielectric constant. By observing the microstructure using plan-view and cross-section transmission electron microscopy, we identified local strain associated with a threading dislocation density on the order of 1011 cm−2 as a possible mechanism for dielectric degradation in these films.

The effect of various substrates on the electrical and electromechanical properties of 100-nm-thick epitaxial 0.9[Pb(Mg1/3Nb2/3)O3]–0.1[PbTiO3](0.9PMN–0.1PT) thin films is investigated. (001) 0.9PMN–0.1PT films are grown on (001)LaAlO3(LAO), (La, Sr)(Al, Ta)O3(LSAT), SrTiO3(STO), and MgO substrates with 40-nm-thick top and bottom La0.5Sr0.5CoO3 electrodes by pulsed laser deposition. X-ray diffraction results indicate that the films on LAO, LSAT, and STO are stressed biaxially in compression in the film-substrate interface whereas the films on MgO are stressed in tension. A decrease in the temperature of dielectric maximum (Tm) together with an increase in the dielectric constant and the longitudinal piezomodulus is observed with decreasing in-plane epitaxial stresses for LAO, LSAT, and STO substrates. The films on MgO substrates have the highest dielectric constant and piezomodulus with Tm below room temperature. The variation in Tm may be attributed to the shift in the transformation temperature from the...

The effect of heteroepitaxy-induced constraint on the structure and piezoelectric properties of the relaxor ferroelectric lead magnesium niobate–lead titanate (PMN–PT) were investigated. Relaxor PMN–PT epitaxial thin films with oxide electrodes were grown by pulsed-laser deposition on (100) LaAlO3 substrates. We observe a systematic decrease in the phase transition temperature (temperature at which a maximum in dielectric response occurs), from around 250 to around 60 °C as the relaxor thickness is increased from 100 to 400 nm. This is accompanied by an increase in the relative dielectric constant (er), measured at room temperature and 10 kHz, from 300 to 2000. The piezoelectric coefficient d33 measured using a scanned probe microscope, increase by almost an order of magnitude with increasing film thickness.

Magnetic force microscopy of amorphous compressed Terfenol‐D films of micron thickness on both crystalline Si and glassy silica shows that their ferromagnetic domain structure is one dimensional and periodic. On Si the structure is aligned with respect to the easy elastic direction of the substrate. The square of the domain period is proportional to the thickness of the film. All facts indicate that the domain morphology in these films is determined by a substantial elastic contribution to the domain wall and film/substrate interaction energies.

Flux trapping in single crystals of YBa2Cu3O7−x before and after twin removal has been measured for vortices parallel and perpendicular to the c axis. The results show clearly that, for low applied magnetic fields, twins contribute significantly to flux pinning over the temperature range 60 to 85 K when the vortices are parallel to the twin boundaries (i.e., parallel to the c axis).

Ag nanostructures were formed along the interface between Ag foil and Si wafer. These structures form when heated in the presence of air below the melting temperature of Ag, while heating above the melting temperature results in Ag foil melting with no nanostructure growth. Nanostructure morphology is determined by Si wafer orientation, while the size and periodicity of the structures depend on the duration of thermal processing. Electron backscatter diffraction (EBSD) analysis shows an epitaxial relation between Ag nanostructures and Si. Annealing specimens in vacuum above the Ag-Si eutectic but below pure Ag melting temperature results in solidification of melted foil without any interfacial nanostructure growth.

The concept of elastic domains is extended to heterophase ferroelectric epitaxial films undergoing phase transformation. Equilibrium nanostructure of ferroelectric phases forming heterophase polydomains, including their relative domain fraction, the distortion of phases, and the orientation of domain interfaces, is determined. The enhanced field induced response of polydomain nanostructures to external field due to domain interface movement is estimated. As an example, rhombohedral-tetragonal polydomain nanostructures in ferroelectric BiFeO3 film are considered.

Functional materials with nonlinear dielectric response are ideally suited for telecommunications applications and threat detection in beam-steering and frequency tuning devices. Developing the theory of wedge domain in graded ferroelectrics, we present herein a quantitative model of domain evolution and dielectric response of compositionally graded ferroelectric multilayers. We show that the domain structure adapts itself to the applied electric field via domain modification. As the applied field rises, the domains are swept away layer by layer resulting in a strong nonlinear field dependence of the dielectric constant and tunability of the multilayers. There is approximately a fivefold improvement in the small-signal dielectric response and threefold enhancement in the dielectric tunability at 400 kV cm−1 in compositionally graded (001) BaxSr1−xTiO3 [BST x/(1−x)] compared to homogeneous BST layers on (001) SrTiO3 substrate. We also demonstrate that by controlling the relative thicknesses of the layers t...

Reversible deformation through the thickness of a compositionally graded shape memory alloy (SMA) film was observed at the nanoscale. Recovery of deformation caused by nanoindentation was characterized at low temperature using atomic force microscopy with in situ heating and cooling. The film was indented at various depths so recovery due to martensite transformations through the thickness could be studied. Tests performed on a homogenous SMA film showed that the recovery exhibited a one-way shape memory effect. The compositionally graded SMA film exhibited a two-way shape memory effect resulting from the variation in the coexistence of the martensite and austenite phases.

Thermodynamic analysis of a graded ferroelectric epitaxial film demonstrates that in the equilibrium state the films subdivide into an alternation of polydomain bands consisting of wedge- or lens-shape domains and single-domain bands. Polarization under an external electrical field proceeds through an interband boundary movement due to the growth/shrinkage of the wedge domains. The domain structure and its evolution are determined by the distribution of the spontaneous polarization and dielectric constant. Through film grading, it is possible to design a controlled domain structure with desirable tunability. Graded films exhibit a sharp increase of the dielectric constant as electrical field approaches zero.

The morphology and structure of interfaces in PbTiO3–CoFe2O4 films on SrTiO3 substrates of various orientations are studied. It is found that for film with thickness more than 100 nm with columnar two-phase morphology, the average orientations of the interfaces between the phases reside on the {110}, {111}, and {112} planes for films normal to substrates oriented along ⟨001⟩, ⟨110⟩, and ⟨111⟩ correspondingly. These macroscopic interfaces consist of {111} nanofacets. The study of very thin film less than 30 nm shows that the interfaces between nanosize phases are {111} planes. Available theoretical results on morphology of multiferroic thin film nanostructure allow us to conclude that for thick films (>100 nm), two-phase columnar morphology (shape of constituent phases, their arrangement, and average crystallographic orientations of the interfaces) is essentially determined by the trend for minimization of elastic energy, while the trend to minimize the energy of interfaces results in faceting interfaces a...

Piezoelectric properties of PbTiO3 in 1/3PbTiO(3)-2/3CoFe(2)O(4) transverse epitaxial nanostructures on differently oriented SrTiO3 were analyzed using conventional and switching-spectroscopy piezoelectric force microscopy. The results confirmed that the individual PbTiO3 nanocolumns in the CoFe2O4 matrix exhibit a detectable piezoelectric response regardless of substrate orientation. For the 100\ and 110\ orientations, a bias of +/- 10 V produced ferroelectric domain switching; however, no switching was observed for the 111\ films. Small values of piezoelectric constants d(zz)((100))approximate to 11 pm/V, d(zz)((110))approximate to 5 pm/V, and d(zz)((111))approximate to 3pm/V are attributed to the weak intrinsic response of the nano-PbTiO3 under strong mechanical and depolarizing-field constraints in the composite films. (c) 2008 American Institute of Physics. Author has checked copyright 11/12/13 RB

The domain structure in bilayer ferroelectric films was studied by using an analytical thermodynamic theory and computer simulations utilizing the phase field model. It is demonstrated that in a low applied field, a self-poled state can be produced in a bilayer film with one layer in a polydomain state and the other layer in a single-domain state. The presence of the layer with a polydomain structure results in a higher dielectric constant and lower coercive field as compared to a bilayer in a single-domain state. The increase in the applied field results in the transition to a single-domain state in the whole bilayer. The thermodynamic potentials of the layers and the energies of electrostatic and elastic interactions determine the critical fields which can control the transitions between single-domain and polydomain states as well as polarization switching of bilayers. Different thermodynamic hysteresis loops are obtained depending on the relationship between these critical fields and the amplitude of the applied ac field. The phase field model of the domain structure produces results that confirm main predictions of the analytical theory.

Graded shape memory alloy thin films were fabricated and characterized to study the effects of compositional gradients on elastic modulus and hardness measurements. Ni47Ti53(at.%) films of varying thickness were deposited onto Ni56Ti44 substrates using dc magnetron sputtering. The films were annealed, producing a compositional gradient across the film-substrate interface through diffusion modification. Nanoindentation measurements were used to characterize the mechanical properties at various depths relative to the film-substrate interface. Before annealing, the dependence of elastic modulus and hardness on relative indentation depth was self-similar for films of different thicknesses due to substrate effects of a two layer system. Annealing allows the diffusion across the film-substrate interface to fully or partially penetrate the film, depending on the thickness of the sputtered layer. The fully penetrated thinner annealed films also display the self-similar behavior of a two layer system. This self-si...

Variable-temperature x-ray diffraction was used to investigate the internal strains that arise from a ferroelectric phase transition in self-assembled multiferroic nanostructures CoFe2O4–PbTiO3 on (001) SrTiO3. The constraints from CoFe2O4 suppressed the c∕a ratio in tetragonal PbTiO3 (without affecting its Curie temperature) while the expansion of the out-of-plane lattice parameter in PbTiO3 upon the transition induced tensile out-of-plane strain in CoFe2O4. The transformation strain was partly relieved by the 90° twin domains in PbTiO3 which reduced the net deformation of the component phases. Significant fractions of both c- and a-domains were observed despite the nanoscale of PbTiO3 in the composite films.

Thermodynamic analysis shows that 180° ferroelectric domains under an external electric field behave as elastic domains due to the converse piezoelectric effect. The interdomain elastic interaction between 180° ferroelectric domains is an important factor in determining the effective dielectric and piezoelectric responses of thin film constrained by a substrate and therefore cannot be neglected.

The equilibrium domain structure and its evolution under an electric field in ferroelectric bilayers and graded multilayers are considered. The equilibrium bilayer is self-poled and contains a single-domain and a polydomain (with 180 domains) layers. The polarization of a graded multilayer proceeds by movement of wedge-like domains as a result of progressive transformation of polydomain layers to a single-domain state. The theory provides the principal explanation of peculiarities of dielectric behavior of graded ferroelectric films and can be applied to graded ferromagnetics and ferroelastics., Comment: 4 pages, 3 figures

A thermodynamic model is presented that describes the polarization and the dielectric response of ferroelectric-paraelectric bilayers and multilayers. It is shown that a strong electrostatic coupling between the layers results in the suppression of ferroelectricity at a critical paraelectric layer thickness. The 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. A numerical analysis is carried out for a pseudomorphic (001) BaTiO3∕SrTiO3 heteroepitaxial bilayer on (001) SrTiO3 and a stress-free BaTiO3∕SrTiO3 bilayer. Complete polarization suppression and a dielectric peak are predicted to occur at approximately 66% and 14% of SrTiO3 in these two systems, respectively.

The effect of substrate orientation on the morphologies of epitaxial self-assembled nanostructures was demonstrated using multiferroic 0.67PbTiO3-0.33CoFe2O4 thin films. The two-phase composite films were grown by pulsed laser deposition on single crystal SrTiO3 substrates having (001) and (110) orientations. The nanostructures of both orientations consisted of vertical rod- or platelet-like columns of CoFe2O4 dispersed in a PbTiO3 matrix. For the (001) orientation the platelet habits were parallel to the {110} planes, whereas for the (110) orientation the platelets were parallel to the {111} planes. The differences were explained using a thermodynamic theory of heterophase structures.

The converse longitudinal piezoelectric responses of PbZr0.2Ti0.8O3∕SrTiO3∕Si heterostructures have been studied for continuous films and for islands patterned by focused ion beam milling (typical dimension is 1×1×1μm). The intrinsic piezoelectric response of the island with an immobile polydomain structure is modeled using finite element analysis. The difference between the results of experimental measurement and modeling is explained by an extrinsic contribution to the piezoresponse from 90° domain movement. The contribution of 90° domain movement to the total piezoresponse is shown to be greatly enhanced in the patterned islands, and leads to an effective piezoelectric coefficient (∼400pm∕V) which is five times larger than the theoretical bulk single domain value.

As a function of film orientation, the intrinsic effective piezoelectric coefficient e31,f is generally formulated for a substrate-constrained ferroelectric film. Numerical results are obtained for Pb(ZrxTi1−x)O3 (PZT) thin films with tetragonal and rhombohedral compositions. It is illustrated that the optimal orientation for e31,f are close to [001] orientation in both tetragonal and rhombohedral PZT films and the maximum calculated e31,f is about −30C∕m2 on the rhombohedral side of the morphotropic phase boundary.

Landau–Devonshire-type phenomenological thermodynamic theory is employed to explain the electric field dependence of piezoelectric properties of tetragonal single domain PbZrxTi1−xO3 (PZT). The strong nonlinearity of the converse piezoelectric coefficient under a large external electric field is proved to be intrinsic both in bulk crystal and epitaxial tetragonal PZT thin films. The tunability of piezoelectric responses by an external electric field and its dependence on the film/substrate misfit and elastic compliance of thin films are characterized quantitatively. The theoretical predictions are in good agreement with the experimental results of piezoresponse scanning microscopy. Due to the large tunability of piezoresponse in it, PZT 50/50 (x=0.5) epitaxial film is a promising candidate for use in future tunable devices.