Phenomenological Landau-Devonshire Theory Research Articles

The Electronic and Ferroelectric Properties in Strontium and Zirconium Doped BaTiO3 from First-Principles Calculations

The structure, electronic and ferroelectric properties of BSZT were investigated based on first-principles calculations. The result of relaxation structure and two-dimensional charge density indicates that the tetragonal crystalline structure is distorted after Sr and Zr doping. The double-well curve fits well with the phenomenological Landau-Devonshire theory. Moreover, the smaller Zr ion displacement leads to a lower spontaneous polarization of BSZT than the original BaTiO3. The hybridization between the 3d states of Ti and the 2p states of O, and the hybridization between the 4d states of Zr and the 2p states of O are observed in the density of states, which is the reason for the ferroelectricity of BSZT materials.

Suppression of vortex–antivortex structures by anti-trimer point defects in hexagonal manganites

The topologically protected vortex–antivortex (V–AV) domain structure in ferroelectric hexagonal manganites has been highly concerned recently, but its stability against intrinsic defects remains to be understood, given the claim that a topological structure would be robust against defects and other perturbations. In fact, it is also known that the V–AV structure is sensitive to the sample quality, and such a well-developed structure is hardly observed in thin films and defective single crystals. In this work, we investigate the influence of anti-trimer point defects on the stability of the V–AV domain structure by employing the phase-field simulation based on the Landau–Devonshire phenomenological theory. It is revealed that the characteristic V–AV structure essentially relies on the anti-trimer point defects under consideration. These defects lower the trimerization transition temperature on one hand and produce pinning effect on the vortex cores/walls on the other hand. However, the V–AV structure does remain robust if the anti-trimer magnitude of these defects is relatively weak but will be eventually destroyed if the anti-trimer magnitude is strong.

Phase diagrams classification based on machine learning and phenomenological investigation of physical properties in K1 − xNaxNbO3 thin films

In this work, we have predicted and classified the temperature-misfit strain phase diagrams of (001)-oriented K1 − xNaxNbO3 (KNN, 0 ≤ x ≤ 0.5) thin films using three classical machine learning algorithms: k-nearest neighbors, support vector machine, and deep neural networks, which have a very excellent prediction accuracy rate of about 99%. Furthermore, various physical properties including ferroelectric, dielectric, piezoelectric, and electrocaloric properties have been calculated and studied based on the phenomenological Landau–Devonshire theory. The calculated results show that the dielectric constant ɛ33, piezoelectric coefficient d33, and isothermal entropy change ΔS of the KNN thin films can be enhanced at the orthorhombic–rhombohedral phase boundary. This work will provide theoretical guidance for experimental studies of KNN thin films.

Statistical thermodynamics of uniaxial ferroelectric: exactly solved model

A detailed analysis of the thermodynamic properties of uniaxial ferroelectrics is carried out within the framework of an exactly soluble model with an infinite radius of interactions. The free energy of a ferroelectric in a power series in the order parameter is expanded and it is shown that all the coefficients of even degree depend strongly on temperature, including the change of their signs at temperatures below the Curie point. The equation of state of a ferroelectric in an external field is derived. A relationship between the width of the zone of metastable states of the ferroelectric and the temperature interval is established. An expression is derived for the height of the energy barrier separating the metastable and stable states of a ferroelectric. The results obtained within the framework of the exact solution of the model are compared with the results within the framework of the Landau-Devonshire phenomenological theory. It is shown that for dimensionless temperatures any Landau-like polynomial approximations for free energy lead to significant errors both in calculating the free energy and in calculating the equilibrium values of the order parameter.

Wide Electrocaloric Temperature Range Induced by Ferroelectric to Antiferroelectric Phase Transition

The ferroelectric (FE) to antiferroelectric (AFE) phase transition tuning the temperature range of electrocaloric (EC) effects was investigated using phenomenological Landau–Devonshire theory. Contrary to ferroelectric to paraelectric (PE) phase transitions for electrocaloric effects, the ferroelectric to antiferroelectric phase transition was adopted to obtain large entropy changes under an applied electric field in a Sm-doping BiFeO3 system. In addition, the doping composition and hydrostatic pressure was observed to tune the ferroelectricantiferroelectric–paraelectric phase transition temperatures and broaden the operating temperature range of electrocaloric effects. The optimal wide temperature range of ~78 K was observed at 3 GPa compressive hydrostatic pressures and 0.05 Sm-doping BiFeO3. The present study paves the way to designing high efficiency cooling devices with larger operating temperature spans.

A thermodynamic potential for barium zirconate titanate solid solutions

Barium zirconate titanate [Ba(ZrxTi1−x)O3] solid solutions are promising lead-free ferroelectric materials that have received substantial interest. Thermodynamic analysis based on phenomenological Landau–Devonshire theory is a powerful method for theoretical investigation of ferroelectric materials, but cannot be applied to Ba(ZrxTi1−x)O3 because there is no thermodynamic potential. In this paper, a thermodynamic potential for Ba(ZrxTi1−x)O3 (0 ≤ x ≤ 0.3) solid solutions is constructed, and then a thermodynamic analysis carried out. The results accurately reproduce known phase structures and their transition temperatures, with good agreement with experimentally measured polarization, dielectric, and piezoelectric constants. It is found that Ba(ZrxTi1−x)O3 solid solutions at room temperature have three phase boundaries, including a tetragonal–orthorhombic phase boundary at x = 0.013, an orthorhombic–rhombohedral phase boundary at x = 0.0798, and a rhombohedral–paraelectric phase boundary at x = 0.2135. The results also indicate that the chemical composition-induced ferroelectric–paraelectric phase boundary has superior electromechanical properties, suggesting a new way to enhance electromechanical coupling in Ba(ZrxTi1−x)O3 solid solutions.

Phase diagram and physical properties of (110) oriented Ba(Zr0.08Ti0.92)O3 thin film

A phenomenological Landau-Devonshire theory is applied to construct the thermodynamic potential of (110) oriented Ba(Zr0.08Ti0.92)O3 thin film and investigate the phase transition, ferroelectric, dielectric and piezoelectric properties. Three ferroelectric phases, such as tetragonal a1 phase, orthorhombic a2c and triclinic γ phase are stable in “misfit strain-temperature” phase diagram. Two triple points are found in the phase diagram and 90° polarization switching can occur directly between tetragonal a1 phase and orthorhombic a2c phase. Complicated phase transitions are induced by the electric field in triclinic γ phase due to the nonlinear coupling terms appeared in the thermodynamic potential. The longitudinal piezoelectric coefficient of (110) oriented Ba(Zr0.08Ti0.92)O3 thin film is smaller than that of (001) oriented film. Moreover, negative longitudinal piezoelectric coefficient can be obtained in triclinic γ phase.

Electrocaloric effects of bulk and thin film Ba(Zr0.08Ti0.92)O3 single crystals

The phenomenological Landau-Devonshire theory is applied to investigate the electrocaloric effects of bulk and thin film Ba(Zr0.08Ti0.92)O3 single crystals. The electrocaloric coefficient of 1.36 × 10−3 C/m2K and adiabatic temperature change of 1.0 °C are obtained in tetragonal T phase for bulk Ba(Zr0.08Ti0.92)O3 single crystal with the electric field of 50 kV/cm and field change of 200 kV/cm, respectively. Ba(Zr0.08Ti0.92)O3 thin film with tensile misfit strain has the larger electrocaloric effect in monoclinic M2 phase than that of tetragonal T phase which exists in compressive misfit strain. The compressive misfit strain does not change the maximum of electrocaloric coefficient, but enlarges the maximum of adiabatic temperature change. However, the tensile misfit strain improves the maxima of electrocaloric coefficient and adiabatic temperature change. In addition, the effects of electric field and temperature on electrocaloric effect are studied in tetragonal T phase and monoclinic M2 phase with different compressive and tensile misfit strains respectively. The large electrocaloric coefficient and adiabatic temperature change at the misfit strain of 0.4% are 7.4 × 10−3 C/m2K and 20 °C for Ba(Zr0.08Ti0.92)O3 thin film with the electric field of 50 kV/cm and the field change of 200 kV/cm, respectively. The giant electrocaloric effect in Ba(Zr0.08Ti0.92)O3 thin film may provide the potential for practical cooling device applications.

Piezoelectric and pyroelectric properties of (001) oriented KNbO3 film

A phenomenological Landau-Devonshire theory is used to investigate the “misfit strain-temperature” phase diagram and physical properties of (001) oriented KNbO3 film. Three ferroelectric phases, such as c phase, aa phase, and γ phase, occur in the phase diagram. In-plane compressive misfit strain is beneficial to form c phase and tensile strain makes aa phase stable. Physical properties of KNbO3 film largely depend on misfit strain and electric field. At room temperature, γ phase of KNbO3 film with the tensile misfit strain has larger piezoelectric and pyroelectric coefficients than that of c phase with the compressive strain. Large piezoelectric and pyroelectric coefficients are 180 pm/V and 8.5 × 10−4 C/m2K respectively at the electric field of 100 KV/cm and misfit strain of 6.7 × 10−3, which are comparable with the experimental results of Pb(ZrxTi1−x)O3 film. Therefore, choosing the appropriate substrates can be used to improve the physical properties of KNbO3 film. In addition, the applied electric field decreases the dielectric, piezoelectric and pyroelectric properties of (001) oriented KNbO3 film.

Phase diagram and physical properties of (110) oriented KNbO3 film

Based on the phenomenological Landau-Devonshire theory, the phase diagram and physical properties of (110) oriented KNbO3 film are investigated. The “misfit strain-misfit strain” phase diagram at room temperature is constructed in the frame of eighth-order thermodynamic potential. Three tetragonal phases and two orthorhombic phases are stable in phase diagram due to the strain anisotropy. The large in-plane compressive or tensile misfit strains favor the tetragonal phases. Moreover, both the tensile misfit strain u1 (or u2) and compressive strain u2 (or u1) induce the orthorhombic phases. Large piezoelectric coefficient is obtained in orthorhombic phases which have the small in-plane tensile misfit strains. It makes (110) oriented KNbO3 film suitable for applications in electromechanical devices.

Orientation dependence of phase diagrams and physical properties in epitaxial Ba0.6Sr0.4TiO3 films

Orientation dependence of phase diagrams and physical properties of Ba0.6Sr0.4TiO3 films are investigated by using a phenomenological Landau-Devonshire theory. New ferroelectric phases, such as the tetragonal a1 phase and the orthorhombic a2c phase in (110) oriented film and the monoclinic MA phase in (111) oriented film, appear in the “misfit strain-temperature” phase diagrams as compared with (001) oriented film. Moreover, the phase diagrams of (110) and (111) oriented films are more complex than that of (001) oriented film due to the nonlinear coupling terms appeared in the thermodynamic potential. The dielectric and piezoelectric properties largely depend on the misfit strain and orientation. (111) oriented film has the better piezoelectric property than (110) oriented film. Furthermore, the compressive misfit strain is prone to induce the larger piezoelectric property than tensile misfit strain.

Giant piezoelectric property of (110) oriented [formula omitted] films

A phenomenological Landau-Devonshire theory is applied to investigate the phase diagrams and physical properties of (110) oriented BaxSr1−xTiO3 films. New ferroelectric phases, such as the tetragonal a1 phase and the orthorhombic a2c phase, appear in the “misfit strain-temperature” phase diagrams for (110) oriented films compared with that of (001) oriented films. Moreover, the orthorhombic a2c phase, and the tetragonal c phase and the triclinic γ phase are stable at low temperature for x=0.5 and x=0.7, respectively. The ferroelectric, dielectric, and piezoelectric properties strongly depend on the misfit strain and electric field. (110) oriented Ba0.7Sr0.3TiO3 film has the larger ferroelectric polarization and piezoelectric coefficient than that of Ba0.5Sr0.5TiO3 film. The giant piezoelectric coefficient of 340pm/V is obtained at the electric field of 50KV/cm in (110) oriented Ba0.7Sr0.3TiO3 film, which is comparable with the values of Pb(Zr1−xTix)O3 and (1−x)Pb(Mg1/3Nb2/3)O3−xPbTiO3 films. It makes (110) oriented BaxSr1−xTiO3 films suitable for applications in electromechanical devices.

Domain structures in circular ferroelectric nano-islands with charged defects: A Monte Carlo simulation

The pattern evolution of striped and vortex domain structures in circular ferroelectric nano-islands with in-plane polarization and charged defects is investigated using the Monte Carlo simulation based on the Landau-Devonshire phenomenological theory. The domain structures of islands undergoing different annealing processes are compared. Given embedded charge carriers at the center of islands, the domain patterns would be markedly affected as a result of the competition and balance between the electrostatic charge energy and other free energy terms in the Landau-Devonshire phenomenological theory. The symmetry of islands with different sizes and charge quantities is also analyzed. The present work provides a simple explanation of a variety of ferroelectric nano-islands and proposes an alternative promising approach to tune the domain structures and symmetry for the applications of nano-sized ferroelectric devices.

Phase diagrams and physical properties of (111) orientedPb(Zr1−xTix)O3thin films

Abstract Based on the phenomenological Landau–Devonshire theory, the phase diagrams and physical properties of (111) oriented Pb ( Zr 1 − x Ti x ) O 3 thin films are investigated. The “misfit strain-temperature” phase diagrams of (111) oriented thin films are more complex than that of (001) oriented thin films due to the appearance of nonlinear coupling terms in the thermodynamic potential. The monoclinic MA phase, the triclinic γ phase, the orthorhombic O phase, and the cubic C phase are stable. The compressive misfit strain induces the monoclinic MA phase, meanwhile the tensile misfit strain is beneficial to make the triclinic γ phase and the orthorhombic O phase stable. The ferroelectric and dielectric properties are calculated which are in great agreement with the experimental measurements. Moreover, the Pb ( Zr 0.5 Ti 0.5 ) O 3 thin films with the Ti composition around the morphotropic phase boundary (MPB) have the large longitudinal dielectric and piezoelectric properties which are in accordance with the other theoretical results. Most importantly, the tensile misfit strain is prone to induce the larger dielectric and piezoelectric properties than that of compressive misfit strain, which may provide the guidance for experimental research.

Antiferroelectric polarization switching and dynamic scaling of energy storage: A Monte Carlo simulation

The polarization-electric field hysteresis loops and the dynamics of polarization switching in a two-dimensional antiferroelectric (AFE) lattice submitted to a time-oscillating electric field E(t) of frequency f and amplitude E0, is investigated using Monte Carlo simulation based on the Landau–Devonshire phenomenological theory on antiferroelectrics. It is revealed that the AFE double-loop hysteresis area A, i.e., the energy loss in one cycle of polarization switching, exhibits the single-peak frequency dispersion A(f), suggesting the unique characteristic time for polarization switching, which is independent of E0 as long as E0 is larger than the quasi-static coercive field for the antiferroelectric–ferroelectric transitions. However, the dependence of recoverable stored energy W on amplitude E0 seems to be complicated depending on temperature T and frequency f. A dynamic scaling behavior of the energy loss dispersion A(f) over a wide range of E0 is obtained, confirming the unique characteristic time for polarization switching of an AFE lattice. The present simulation may shed light on the dynamics of energy storage and release in AFE thin films.

Dielectric and piezoelectric properties of (110) oriented Pb(Zr1−xTix)O3 thin films**Project supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, the Research Fund of Jiangsu Province Cultivation Base for State Key Laboratory of Photovoltaic Science and Technology, China, Major Projects of Natural Science Research in Jiangsu Province, China (Grant No. 15KJA43002), and Qing Lan Project of Education

A phenomenological Landau–Devonshire theory is developed to investigate the ferroelectric, dielectric, and piezoelectric properties of (110) oriented Pb(Zr1−xTix)O3 (x = 0.4, 0.5, 0.6, and 0.7) thin films. At room temperature, the tetragonal a1 phase, the orthorhombic a2c phase, the triclinic γ1 phase, and the triclinic γ2 phase are stable. The appearance of the negative polarization component P2 in the a2c phase and the γ1 phase is attributed to the nonlinear coupling terms in the thermodynamic potential. The γ phase of the Pb(Zr1−xTix)O3 thin films has better dielectric and piezoelectric properties than the a2c phase and the a1 phase. The largest dielectric and piezoelectric coefficients are obtained in the Pb(Zr0.5Ti0.5)O3 thin film. The piezoelectric coefficient of 110–150 pm/V is obtained in the (110) oriented Pb(Zr0.5Ti0.5)O3 thin film, and the Pb(Zr0.3Ti0.7)O3 thin film has the remnant polarization and relative dielectric constant of 50 μC/cm2 and 100, respectively, which are in agreement with the experimental measurements reported in the literature.

Nature of ferroelectric-paraelectric phase transition and origin of negative thermal expansion inPbTiO3

Ferroelectric-paraelectric (FE-PE) phase transitions have been primarily explained by the phenomenological Landau-Devonshire theory and a soft-zone-center mode of vibration in the literature. In this work, we study the atomic structure and polarization evolution of $\mathrm{PbTi}{\mathrm{O}}_{3}$ as a function of temperature using ab initio molecular dynamics simulations. In contrast to conventional molecular dynamics analyses where results are averaged over time, we categorize the atomic configurations as a function of time in terms of Ti-O bond lengths in the nearest-neighboring shell. We show that an appreciable amount of cubic configuration exists at temperatures about 300 K below its FE-PE phase transition temperature of 763 K, even though the time-averaged overall atomic configuration is tetragonal. The quantitative results depict that as the temperature increases the population of the cubic configuration increases and that of the tetragonal configuration decreases, signifying that the FE-PE phase transition is intrinsically second order. It reveals that the thermal fluctuation of the cubic configurations in the tetragonal matrix makes a significant contribution to the negative thermal expansion in the FE phase region because the cubic configuration has smaller volume and higher entropy than the tetragonal matrix.

Domain splitting and enhanced piezoelectricity in ferroelectric thin films with square grid structure

The pattern evolution of the stripe-like domain structure in tetragonal ferroelectric thin films upon introduction of square void arrays is investigated using Monte Carlo simulation based on the Landau-Devonshire phenomenological theory. The regular splitting of the stripe-like domains near the voids and substantial release of both the dipole-dipole interaction and the electromechanical energy are revealed. Consequently, a significant enhancement of piezoelectric coefficient is predicted. It is suggested that the delicate balance between the two energy terms modulated by the void array periodicity and void size is responsible for the domain splitting. The present work proposes an alternative promising approach to tune the domain structure via simple micro-fabrication techniques.

Permittivity changes induced by injected electrons and field-induced phase transition in KTa1−xNbxO3 optical beam deflectors

A space-charge-controlled optical beam deflector made of a KTa1−xNbxO3 (KTN) single crystal utilizes electrons that are injected through the cathode by applying voltage. With the deflector made of lithium-doped KTN (K0.95Li0.05Ta0.73Nb0.27O3, KLTN/0.05/0.27), we observed large increases in the capacitance of the deflector when we injected electrons. The increases were not caused by changes in the electrode interface but by changes in the permittivity of the bulk crystal. In the paraelectric phase, the KLTN/0.05/0.27 crystal exhibited nonlinearity in the dielectric response with double hysteresis loops in the D–E curves. We ascribed the permittivity change to this nonlinear phenomenon. We also discuss this nonlinearity in terms of the Landau–Devonshire phenomenological theory. The coefficient g4 of the fourth power term in the expanded free energy was negative in the paraelectric phase near the phase transition temperature as it is for other materials that exhibit a first-order phase transition. However, g4 depended on the temperature and its sign became positive about 15 °C above the phase transition temperature.

COMBINED EFFECT OF THE ELECTRODE AND SURFACE TRANSITION LAYER ON THE PROPERTIES OF A FERROELECTRIC THIN FILM

Within the framework of the modified Ginzburg–Landau–Devonshire phenomenological theory, we study the properties of a ferroelectric thin film with surface transition layer, considering the effect of electrodes. The combined effect of the electrode and surface transition layer on the properties (including the polarization, transition temperature and coercive filed) of a ferroelectric thin film is discussed in detail. The results show that the surface transition layer and the electrode can induce the phase transition from ferroelectric to paraelectric phase.