Misfit Strain-temperature Phase Diagrams Research Articles

Misfit-Strain Phase Diagram, Electromechanical and Electrocaloric Responses in Epitaxial PIN-PMN-PT Thin Films.

xPb(In1/2Nb1/2)O3-(1-x-y)Pb(Mg1/3Nb2/3)O3-yPbTiO3 (PIN-PMN-PT) bulks possess excellent electromechanical coupling and dielectric properties, but the corresponding epitaxial PIN-PMN-PT thin films have not yet been explored. This paper adopts a nonlinear thermodynamics analysis to investigate the influences of misfit strains on the phase structures, electromechanical properties, and electrocaloric responses in epitaxial PIN-PMN-PT thin films. The misfit strain-temperature phase diagram was constructed. The results reveal that the PIN-PMN-PT thin films may exist in tetragonal c-, orthorhombic aa-, monoclinic M-, and paraelectric PE phases. It is also found that the c-M and aa-PE phase boundaries exhibit a superior dielectric constant ε11 which reached 1.979 × 106 with um = -0.494%, as well as the c-M phase boundary showing a large piezoelectric response d15 which reached 1.64 × 105 pm/V. In comparison, the c-PE and M-aa phase boundaries exhibit a superior dielectric constant ε33 over 1 × 105 around um = 0.316% and the piezoelectric response d33 reached 7235 pm/V. The large electrocaloric responses appear near the paraelectric- ferroelectric phase boundary. These insights offer a guidance for experiments in epitaxial PIN-PMN-PT thin films.

Phase diagrams and electromechanical properties of polydomain epitaxial (1−x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 thin films

Ferroelectric thin films usually exhibit polydomain structures, while current thermodynamics analysis on (1−x)Pb(Mg1/3Nb2/3)–xPbTiO3 [(1−x)PMN–xPT] thin films assumed films only possessing single domain. Thus we predict misfit strain–temperature phase diagrams and electromechanical properties of epitaxial (1−x)PMN–xPT thin films via thermodynamics analysis with polydomain structures taken into account. The results show that polydomain structures are more stable than single domain in most areas, consistent well with experimental observations. Phase diagram for 0.7PMN-0.3PT thin films obviously differs from those for 0.58PMN-0.42PT and 0.3PMN-0.7PT thin films. Excellent electromechanical properties are observed near the phase boundary between c and r 1/r 2 phases in 0.7PMN-0.3PT thin films.

Phase diagram and pyroelectric response of polydomain epitaxial Ba0.6Sr0.4TiO3 thin films

A nonlinear thermodynamic theory is used to investigate the phase structures, polarization and pyroelectric properties of polydomain epitaxial Ba0.6Sr0.4TiO3 thin films. Polydomain a1/a2/a1/a2, ca1/ca2/ca1/ca2, aa1/aa2/aa1/aa2, r1/r2/r1/r2 phases and single domain tetragonal c, paraelectric PE phases have been found in the misfit strain-temperature phase diagram. Note that the polydomain phases are found to be more complicated than single domain phases, which also leads to the variability of pyroelectric properties. The results of pyroelectric coefficients reveal that a distinguished in-plane and out-of-plane pyroelectric response appears near the phase boundaries of a1/a2/a1/a2-PE and ca1/ca2/ca1/ca2-c, c-PE, respectively, in which the pyroelectric coefficients |pi| are larger than 0.6 μC/cm2 K, exceeding most experimental and theoretical values. It is found that the maximum in-plane and out-of-plane pyroelectric coefficients occur under the strain of 0.23% and −0.225% at room temperature, respectively. The giant pyroelectric performance of polydomain Ba0.6Sr0.4TiO3 thin films may provide potential to highly sensitive infrared detectors.

Misfit strain-temperature phase diagram of multi-domain structures in (111)-oriented ferroelectric PbTiO3 films

High-index-oriented epitaxial ferroelectric films have recently attracted great attention due to their emergent functional properties related to the multi-domain structures. Here, the equilibrium phases and domain structures in (111)-oriented ferroelectric PbTiO3 films were investigated via phase-field simulations and the misfit strain-temperature equilibrium phase diagram was constructed. It was found that the epitaxial strain can effectively control the orientations of polarization vectors, which uniquely determine the domain variant patterns, domain wall orientations and densities. In particular, two types of tetragonal-like domain patterns can form under different strains with their distinct structural characteristics, ferroelectric properties and thermal conductivities. These results provide guidance for interpreting and understanding experimental data as well as designing of (111)-oriented ferroelectric films with specified domain structures and properties.

Multicaloric effect in multiferroic EuTiO3 thin films

A modified Landau–Ginzburg–Devonshire phenomenological thermodynamic theory is used to investigate both the influence of biaxial compressive misfit strain between film and the substrate and the mechanical stress on the multicaloric response in epitaxial EuTiO3 thin films. The complicated compressive misfit strain–temperature phase diagram in the low-temperature region is developed. The excellent electrocaloric and elastocaloric effect can be achieved: $$ \Delta T(T_{\text{C}} ) = 3.66\,{\text{K}} $$, while $$ \Delta E = 100\,{\text{kV/cm}},u_{\text{m}} = - \,4.0{\%} $$; $$ \Delta T $$ = 5.31 K at 200 MPa. Besides, the maximal adiabatic temperature change $$ \Delta T(T_{\text{M}} ) = 17.3\,{\text{K}} $$, while $$ \Delta H = 5\,{\text{T}},u_{\text{m}} = - \,4.0{\%} $$, in the low-temperature region, which is comparable with the experimental result. Both the misfit strain and the external mechanical stress play a crucial role in the multicaloric response in EuTiO3 films. It may open more opportunities for practical application in refrigeration devices, especially for low-temperature solid-state multicaloric cooling.

Crystallographic orientation-dependent piezoelectric response in BaTiO3 thin films and the domain evolution under different temperatures

The effects of crystallographic orientation on the domain structures and piezoelectric response of BaTiO3 (BTO) thin films were investigated by piezoresponse force microscopy (PFM) systematically. It is found that the domain structures of BTO films are obviously orientation dependent, and the (111) oriented BTO film shows the best piezoelectric properties. Therefore, the nanoscale polydomain switchings within valid single grains of the BTO(111) thin film were observed by PFM under different temperatures. According to the switching process, the a1/a2c, r/a2c, and a1c/r polydomain states were specially introduced into the theoretical model to describe the temperature-induced polydomain switchings of the BTO(111) thin film. The misfit strain-temperature phase diagram was simulated to present the a1/a2c-r/a2c-a1c/r-p domain switching, which corresponds with the threshold temperature of domain switchings obtained from the experimental results of the BTO(111) thin film.

Ferroelectric domain structures and temperature-misfit strain phase diagrams of K1-xNaxNbO3 thin films: A phase-field study

Potassium-sodium niobate K1-xNaxNbO3 (KNN) is one of the most promising lead-free piezoelectric materials. While there have been many studies on the microstructures and properties of KNN ceramics, the phase transitions and ferroelectric domain structures of KNN thin films are not well understood. In this work, we employ three-dimensional (3D) phase-field simulations to obtain the ferroelectric domain structures of KNN (0 ≤ x ≤ 0.5) thin films under a range of temperatures (0 K to 1300 K) and equiaxial misfit strains (–1.5% to 1.5%), based on which we establish the misfit strain-temperature phase diagrams of KNbO3 and K0.5Na0.5NbO3 thin films. We identify a wide variety of complex domain structures with coexisting ferroelectric phases, implying enhanced dielectric and piezoelectric properties. We expect this work to provide guidance for the strain engineering of domain structures and properties of KNN thin films.

Giant electrocaloric effect in ferroelectric ultrathin films at room temperature mediated by flexoelectric effect and work function

In ferroelectric ultrathin films, built-in electric fields are often present due to the flexoelectric effect and the difference of work functions at asymmetric electrodes, which may change the properties of the materials. In this paper, the influence of build-in electric fields induced by flexoelectric effect and/or work function difference on the misfit strain-temperature phase diagrams, and the electrocaloric properties of epitaxial BaTiO3 ultrathin films are investigated by using an extended nonlinear thermodynamic theory. It is found that the flexoelectric effect, i.e., the coupling of polarization and strain gradient, changes the misfit strain-temperature phase diagrams notably, in which the phases with out-of-plane polarizations increase due to the presence of a built-in field. The electrocaloric properties are remarkably enhanced when the built-in fields induced by both the flexoelectric effect and work function difference are considered. In particular, a giant adiabatic temperature change of 7.89 K in ultrathin Pt/BaTiO3/SrRuO3 capacitors at 460 K is predicted. Moreover, it is demonstrated that the peak of adiabatic temperature change versus working temperature is shifted from a high temperature to room temperature, suggesting that ferroelectric ultrathin films with asymmetric electrodes and strain gradient are promising candidates for room temperature refrigeration.

Phenomenological thermodynamic potentials for bulk and thin-film Ba(Zr0.08Ti0.92)O3 single crystals

Phenomenological thermodynamic analysis is an important theoretical investigation method for ferroelectric materials, however, it cannot be implemented for Ba(ZrxTi1−x)O3 due to the lack of thermodynamic potential coefficients. In this paper, we have constructed a phenomenological thermodynamic potential for bulk Ba(Zr0.08Ti0.92)O3 single crystals, which reproduces the three phase transition temperatures, dielectric and piezoelectric constants of bulk Ba(Zr0.08Ti0.92)O3 single crystals well, suggesting that the constructed thermodynamic potential is reliable. Then the thermodynamic potential with appropriate modification is applied to predict misfit strain-temperature phase diagram and electromechanical properties of Ba(Zr0.08Ti0.92)O3 thin films. It is found that compressive strain favors the tetragonal c phase with an out-of-plane polarization component, while tensile misfit strain favors orthorhombic aa phase with an in-plane polarization component. It also reveals that Ba(Zr0.08Ti0.92)O3 thin films under appropriate compressive strain show higher piezoelectric coefficient d15 than that of their bulk counterpart. The constructed thermodynamic potential opens a new avenue to theoretical analysis on Ba(Zr0.08Ti0.92)O3.

Effect of crystal orientation on the phase diagrams, dielectric and piezoelectric properties of epitaxial BaTiO3 thin films

The influence of crystal orientations on the phase diagrams, dielectric and piezoelectric properties of epitaxial BaTiO3 thin films has been investigated using an expanded nonlinear thermodynamic theory. The calculations reveal that crystal orientation has significant influence on the phase stability and phase transitions in the misfit strain-temperature phase diagrams. In particular, the (110) orientation leads to a lower symmetry and more complicated phase transition than the (111) orientation in BaTiO3 films. The increase of compressive strain will dramatically enhance the Curie temperature TC of (110)-oriented BaTiO3 films, which matches well with previous experimental data. The polarization components experience a great change across the boundaries of different phases at room temperature in both (110)- and (111)-oriented films, which leads to the huge dielectric and piezoelectric responses. A good agreement is found between the present thermodynamics calculation and previous first-principles calculations. Our work provides an insight into how to use crystal orientation, epitaxial strain and temperature to tune the structure and properties of ferroelectrics.

Misfit strain phase diagrams of epitaxial PMN–PT films

Misfit strain–temperature phase diagrams of three compositions of (001) pseudocubic (1 − x)·Pb (Mgl/3Nb2/3)O3 − x·PbTiO3 (PMN–PT) thin films are computed using a phenomenological model. Two (x = 0.30, 0.42) are located near the morphotropic phase boundary (MPB) of bulk PMN–PT at room temperature (RT) and one (x = 0.70) is located far from the MPB. The results show that it is possible to stabilize an adaptive monoclinic phase over a wide range of misfit strains. At RT, the stability region of this phase is much larger for PMN–PT compared to barium strontium titanate and lead zirconate titanate films.

Misfit strain-temperature phase diagrams and domain stability of asymmetric ferroelectric capacitors: Thermodynamic calculation and phase-field simulation

Thermodynamic calculation and phase-field simulation have been conducted to investigate the misfit strain-temperature phase diagrams, dielectric property, and domain stability of asymmetric ferroelectric capacitors (FCs), with considering the effects of dissimilar screening properties and work function steps at the two interfaces. The distinct features of asymmetric FCs from their symmetric counterparts have been revealed and discussed. Polar states with nonzero out-of-plane polarization in parallel with the built-in field are found preferential to form in asymmetric FCs. Meanwhile, the built-in field breaks the degeneracy of states with out-of-plane polarization in anti-directions. This leads to the necessity of redefining phases according to the bistability of out-of-plane polarization. Moreover, the phase stability as well as the dielectric behavior can be significantly controlled by the properties of electrodes, misfit strain, and temperature. The phase-field simulation result also shows that polydomain instability would happen in asymmetric FCs as the equivalence of domain stability in anti-directions is destroyed.

Free-standing ferroelectric multilayers: Crossover from thin-film to bulk behavior

Ferroelectric films usually have phase states and physical properties very different from those of bulk ferroelectrics. Here we propose free-standing ferroelectric-elastic multilayers as a bridge between these two material systems. Using a nonlinear thermodynamic theory, we determine phase states of such multilayers as a function of temperature, misfit strain, and volume fraction φp of passive elastic material. The numerical calculations performed for two classical ferroelectrics—PbTiO3 and BaTiO3—demonstrate that polarization states of multilayers in the limiting cases φp→1 and φp→0 coincide with those of thin films and bulk crystals. At intermediate volume fractions, however, the misfit strain-temperature phase diagrams of multilayers differ greatly from those of epitaxial films. Remarkably, a ferroelectric phase not existing in thin films and bulk crystals can be stabilized in BaTiO3 multilayers. Owing to additional tunable parameter and reduced clamping, ferroelectric multilayers may be superior for a wide range of device applications.

Strain effect on phase transitions of BaTiO3 nanowires

The effects of strain on the phase transitions of BaTiO3 nanowires taking into account three components of polarization are studied by thermodynamic analysis based on the Landau theory. Similar to the strain effect on phase transitions in thin films, the mismatch strain between the nanowire and substrate governs the Curie temperature. The complete misfit strain–temperature phase diagram shows six stable ferroelectric phases for BaTiO3 nanowires under different strain and temperature conditions.

Phenomenological analysis of phase transitions in epitaxial perovskite ferroelectric thin films

A phenomenological Landau–Ginzburg–Devonshire theory is employed to investigate the effect of biaxial misfit strains and in-plane shear strain on thermodynamic equilibrium states and dielectric properties of single domain KNbO 3, BaTiO 3, and PbTiO 3 thin films. For KNbO 3 thin films grown on cubic substrates, the constructed isotropic misfit strain–temperature phase diagram is in qualitative agreement with the result from first-principle calculations. For BaTiO 3 and PbTiO 3, misfit strain–temperature phase diagrams at constant in-plane shear strains are constructed. In-plane shear strain is shown to restrain formation of a phase (polarization along [1 0 0]). The anisotropic misfit strain–temperature and misfit strain–misfit strain phase diagrams are also developed for KNbO 3 thin films grown on orthorhombic substrates. The anisotropic biaxial misfit strains lead to appearance of orthorhombic phases (a 1, a 2) and monoclinic phases (a 1c, a 2c).

Dielectric response and structure of in-plane tensile strained BaTiO3 thin films grown on the LaNiO3 buffered Si substrate

Highly (001)-textured BaTiO3 films were grown epitaxially on the LaNiO3 buffered Si substrate. A strong in-plane tensile strain has been revealed by using x-ray diffraction and high resolution transmission electron microscopy. The BaTiO3 film has exhibited a small remnant polarization, indicating the presence of ca1∕ca2∕ca1∕ca2 polydomain state in the film. Temperature dependent dielectric permittivity has demonstrated that two phase transitions occurred at respective temperatures of 170 and 30°C. The result was discussed in detail based on the misfit strain-temperature phase diagrams theory.

Phase diagrams of single-domain ferroelectric-dielectric superlattices

Using the thermodynamic theory, the authors developed misfit strain-temperature phase diagrams of single-domain ferroelectric-dielectric superlattices grown on cubic substrates. Owing to internal electric fields appearing in such multilayers, the superlattice diagrams are expected to be very different from phase maps of homogeneous ferroelectric films. The calculations show, however, that this electrostatic effect does not change relative positions of phase transition lines. It only shifts the diagram as a whole along the line separating stability ranges of paraelectric phase and in-plane polarization state. The magnitude of this shift is governed by the capacitance of dielectric layer and the thickness of ferroelectric one.

In-plane polarization states and their instabilities in polydomain epitaxial ferroelectric thin films

A Landau–Ginsburg–Devonshire-type thermodynamic theory is used to describe epitaxial ferroelectric films with dense laminar domain structures, where spontaneous polarizations in both domains are oriented in the film plane. For PbTiO3 films, it is found that, at positive misfit strains, the domain patterning transforms the orthorhombic aa phase, which is stable in single-domain films, into a pseudotetragonal a1/a2/a1/a2 polydomain state. In BaTiO3 films, the latter is further replaced at low temperatures by a polydomain aa1/aa2/aa1/aa2 state. With decreasing misfit strain, both a1/a2/a1/a2 and aa1/aa2/aa1/aa2 patterns become unstable with respect to the appearance of polarization component orthogonal to film surfaces. This results in the formation of polydomain states in BaTiO3 films, which do not exist in bulk crystals. The stability ranges of various states in the misfit strain-temperature phase diagram are determined.

Effects of domain formation on the dielectric properties of ferroelectric thin films

A Landau-Ginsburg-Devonshire-type thermodynamic theory is used to describe dense laminar domain structures in epitaxial ferroelectric thin films grown on “tensile” substrates and to compute their small-signal dielectric responses. For PbTiO3 and BaTiO3 films, it is found that the ferroelectric phase transition results in the formation of a pseudo-tetragonal polydomain a 1/a 2/a 1/a 2 state. The stability range of the a 1/a 2/a 1/a 2 structure in the misfit strain-temperature phase diagram is determined. Effects of domain formation on the dielectric properties of ferroelectric films are analyzed by comparing permittivities of polydomain and single-domain films. Theoretical results are compared with the experimental data on (Ba1−xSrx)TiO3 films grown on platinum coated silicon substrates.

Phase transitions and strain-induced ferroelectricity inSrTiO3epitaxial thin films

A Landau-Ginsburg-Devonshire-type theory is used to describe the mechanical substrate effect on equilibrium states and phase transitions in ${\mathrm{SrTiO}}_{3}$ epitaxial thin films. The misfit strain-temperature phase diagram of ${\mathrm{SrTiO}}_{3}$ films is developed taking into account the existence of two coupled instabilities (antiferrodistortive and ferroelectric) in this crystal. It is shown that ${\mathrm{SrTiO}}_{3}$ films remain paraelectric down to 0 K only in a narrow range of small negative misfit strains between $\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\ensuremath{-}2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}.$ Outside this ``paraelectric gap,'' the 2D clamping and straining of the film by the substrate leads to the appearance of ferroelectricity in ${\mathrm{SrTiO}}_{3}$ films. The temperature of the ferroelectric transition increases rapidly outside the aforementioned misfit strain range.