Size-driven Phase Transition Research Articles

Ferroelectric properties in thin film barium titanate grown using pulsed laser deposition

The characteristics of polycrystalline BaTiO3 metal-insulator-metal capacitors, fabricated using pulsed laser deposition, are investigated from room temperature to 420 K. The capacitance–voltage characteristics show ferroelectric behaviour at room temperature, with a phase transition to paraelectric at higher temperature. However, the permittivity response shows paraelectric behaviour across all measured temperatures. So BaTiO3 exists here in a mixture of cubic and tetragonal phases. The BaTiO3 films have a columnar structure, with grain size increasing with film thickness due to their increasing height but not diameter. This correlates with an increase in remnant polarization. The results support a size driven phase transition in thin films of polycrystalline BaTiO3.

Application of Raman Spectroscopy on Size Driven Phase Transition in Bismuth Titanate

Bismuth titanate nano-crystals were prepared successfully by sol-gel method and the critical particle size for phase transition was analyzed by Raman techniques. The results revealed the new Raman peaks at the wave number about 87, 227, 442, 467, 577 and 617cm-1 discerned gradually with increasing the particle size and abrupt increase in integrated intensity ratios of these modes, companied with strong decrease of half-widths happened at the particle size ranging from 18 to 33nm, which suggested an obvious size driven tetragonal-to-orthorhombic phase transition in Bismuth titanate nano-crystals.

Influence of thermal strains on the electrocaloric and dielectric properties of ferroelectric nanoshells

The electrocaloric effect and dielectric tunability of BaTiO3 ferroelectric nanoshells on Si and MgO cores are investigated using the modified Landau–Ginzburg–Devonshire theory, in which the surface tension and thermal strain are taken into account. The numerical results exhibit a peak of electrocaloric coefficient near the critical nanoshell thickness accompanied with the size-driven phase transition. In addition to the enhanced adiabatic temperature difference, the compressive thermal strain also significantly improves the dielectric tunability. More importantly, the ferroelectric nanoshell displays pronounced electrocaloric effect: ΔT(Tm)=2.09 K for the nanoshell on Si core and ΔT(Tm)=2.33 K on MgO core, respectively. Essentially, the ferroelectric nanoshell provides an effective means to acquire good electrocaloric effect and high dielectric tunability by adjusting the wall thickness, core radius, annealing temperature, and various core materials, which may effectively contribute to the stress level in the ferroelectric nanoshell.

Size Effects in Ferroelectric PbTiO3 Nanomaterials Observed by Multi-Frequency Electron Paramagnetic Resonance Spectroscopy

Lead titanate (PbTiO3) micro- and nanocrystalline powders have been prepared from metallo-oranic precursor through combined polymerisation and pyrolysis (CPP). The enhanced liquid-precursor based version of the cpp route in combination with soft milling enables an adjustment of the mean particle size up to 5 nm. A multi-frequency (X, Q, and W band) electron paramagnetic resonance study of Cr-doped micro- and nanocrystalline PbTiO3 samples was performed. Three Cr3+ centers (C1, C2, and C3) with different axial Zero Field Splitting (ZFS) parameters were identified in microcrystalline samples. The center C1 is similar to that observed in previous X band single crystal and ceramic sample measurements. The superposition model by Newman and Urban was applied to translate the ZFS data of these centers into local Cr3+ displacements inside the distorted oxygen octahedra of the microcrystalline PbTiO3 lattice. In the nanocrystalline powders only the center C1 was observed. Its EPR spectra in dependence on the mean particle size were fitted using a spin-Hamiltonian in which a Gaussian distribution of ZFS terms was assumed. The variation of the mean value of ZFS parameter D and distribution width deltaD was determined and the critical particle size of the size-driven phase (tetragonal-cubic) transition was estimated. In nanocrystalline powders with mean particle size d < d(cr) the tetragonal C1 spectrum is not more detectable. A new Cr3+ center spectrum, C4, consisting of a single line with an isotropic g-factor is detectable allowing the cubic phase in the nanomaterials to be quantified. Further, temperature dependent EPR measurements were made which allowed the variation in Curie temperature with mean particle size to be determined.

Hysteresis loops of first-order ferroelectric bilayers or superlattices and their size effect

Based on Landau–Ginzburg phenomenological theory, a first-order ferroelectric bilayer or superlattice with an antiferroelectric interface coupling has been studied by taking into account the spatial variation of polarization within each constituent film and the surface effect. The hysteresis loops are obtained and the size effect of a bilayer is discussed. The loop patterns vary between typically antiferroelectric and typically ferroelectric depending on the thickness ratio, the coupling constant, the thickness and the extrapolation length. The antiferroelectric coupling has a great effect on the phase transition of a bilayer. It is shown that the size-driven phase transition cannot be observed in a ferroelectric bilayer in the case of strong antiferroelectric coupling.

Study of the tetragonal-to-cubic phase transition inPbTiO3 nanopowders

The CPP (combined polymerization and pyrolysis) preparation route, in its enhancedliquid-precursor-based version, was combined with consecutive soft milling. For studies oftemperature- and size-dependent structural changes occurring in ferroelectric lead titanate,this combined route yields a nanopowder series covering the relevant particle-size region attarget quality. This material basis enables consistent SEM, TEM, XRD, Raman,EPR and dielectric measurements, which furnish a comprehensive picture of thecooperation between temperature rise and size reduction to eliminate tetragonality andconcomitant ferroelectricity. Our previous original EPR studies on nanosized bariumtitanate are now extended to the lead titanate case. Furthermore, as comparedto the pertinent literature standard, the materials basis is extended to powdersamples of smaller mean particle sizes, comprising the critical size at which aPbTiO3 particle undergoes a transition into cubic paraelectric phase. Thus, the size-driven phasetransition can be observed in a direct way (at 7 nm, which compares to 40 nm forBaTiO3),and the EPR data suggest a much less spacious gradient shell at the particle surfaces (thickness≈ 2 nm) than in previous analogous investigations onBaTiO3 (15 nm).

Random Field Based Model for Calculation of the Properties of Relaxor Ferroelectric Thin Films

The model of relaxor ferroelectric films is proposed. Its basis is the theory of the random field. It destroys the polar long-range order and transforms it into mixed state of ferroelectric glass (FG) or dipole glass (DG). The spatial distribution of the physical properties of relaxor ferroelectric film was calculated with the random field distribution function. As an example the dependence of the order parameter on film thickness, temperature and distribution function width was obtained. The critical thickness and temperature of the size-driven phase transition from FG to DG state as a function of the film and distribution function were calculated.

Size driven phase transition of barium titanate nanoparticles prepared by plasma chemical vapor deposition

Size driven phase transition of barium titanate nanoparticles prepared by plasma chemical vapor deposition

Nanosize ferroelectric oxides – tracking down the superparaelectric limit

Free ferroelectric nanoparticles in the order of 10 nm undergo a size driven phase transition into a paraelectric phase. However, in all applications, especially in ferroelectric random access memories, ferroelectric nanograins are integrated into a circuit. They are therefore exposed to new electromechanical boundary conditions e.g. substrate strain and screening of the depolarization field in the electrodes. Carefully adapted to the respective material, some of the extrinsic effects can be used to stabilize ferroelectricity and to shrink the ultimate size. The system performance is very sensitive to the fabrication and processing procedures.

The description of size effects in films of order-disorder ferroelectrics on the basis of the renormalized free energy

Films of order–disorder-type ferroelectrics were considered in the mean-field approximation of the Ising model taking into account the depolarization field and four-dipole interactions. It was shown that this system could be described on the basis of the renormalized bulk system free energy with two-dipole interaction constant dependent on the film thickness, surface and depolarization field characteristics. This led to the size-driven phase transition between paraelectric and ferroelectric phases with transition temperature dependent on the film thickness. For small values of the four-dipole interaction constant, the size-driven crossover from the first-order phase transition to the second-order one with film-thickness change was forecasted. An analytical expression for the tricritical point temperature and thickness was obtained. The increase of the four-dipole interaction constant led to the first-order phase-transition existence independently of the film thickness, with the temperature region of the phases' coexistence widening with thickness decrease. The phase diagram in coordinates temperature–film thickness and the order parameter were calculated with the help of the derived free energy. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Investigation of size-driven phase transition in bismuth titanate nanocrystals by Raman spectroscopy

Raman spectroscopy was used to investigate the lattice dynamics and structural transformations in bismuth titanate (Bi4Ti3O12) nanocrystals prepared by a chemical coprecipitation technique. The crystal structure of the samples of different grain sizes was determined by X-ray-diffraction analysis. The evolution of the Raman spectrum with grain size was characterized by an intensity decrease, a broadening of the line width, a frequency shift, and the disappearance of the Raman mode. The results revealed the appearance of a size-driven phase transition from orthorhombic to tetragonal phases at a critical size of 44 nm. This result is quite consistent with the X-ray-diffraction measurement and differential thermal analysis. The origin was attributed to the grain-size effect and explained by the surface-energy mechanism.

Effect of surface tension and depolarization field on ferroelectric nanomaterial properties

AbstractThe theory of size effects in nanocrystalline ferroelectric ceramics or nanoparticle powders allowing for surface tension and depolarization field is proposed. Surface tension was included in the free energy functional and extrapolation length was expressed via surface tension coefficient. The latter was shown to be dependent on temperature due to its relation to the dielectric permittivity of the nanoparticles. The depolarization field effect was calculated in the model taking into account the space‐charge layer on the surface.The Euler–Lagrange equation for inhomogeneous polarization was solved analytically in both paraelectric and ferroelectric phases. The temperature and size dependence of the spontaneous polarization and dielectric susceptibility of nanomaterials was obtained. The possibility to calculate these and other properties by minimization of the conventional free energy in the form of different power polarization series, but with coefficients that depend on particle size, temperature, contribution of depolarization field and surface tension coefficient, was demonstrated. A comparison with available experimental data is performed.

Combined effect of thickness and stress on ferroelectric behavior of thin BaTiO3 films

Thin BaTiO3 (BTO) layers were deposited by magnetron sputtering on a Si substrate between two thin LaNiO3 (LNO) electrodes (LNO/BTO/LNO/Si structure). The thickness of the BTO layer was varied between 35 nm and 1 μm. The stress, dielectric permittivity, and ferroelectric hysteresis loop were measured after deposition and during heating. It was found that the BTO layers are under tensile stress at the Curie temperature. The tensile stress increases with decreasing layer thickness leading to a shift of the Curie point to a lower temperature, a decrease of remanent polarization, and an increase of the coercive field. The effect of tensile stress on the Curie temperature is dominant within a restricted range of stresses between 300 and 450 mega Pascals (MPa), where the Curie temperature decreases linearly by about 0.16 °C/MPa. A good correlation was found between stress and dielectric measurements with respect to the temperature of the Curie point. The ferroelectric hysteresis loops showed that the ferroelectric-paraelectric phase transition starts at the Curie temperature of the BTO layer and continues within a range of temperatures until about the Curie temperature of the bulk BTO material. The ferroelectric behavior indicates dominance of domains within the interior part of the BTO layer and minor contribution of surface domains. The results are compared with a theoretical approach of size-driven phase transition in stress-induced ferroelectric thin films.

Ferroelectric thin film properties—Depolarization field and renormalization of a “bulk” free energy coefficients

We suggest an approach to calculate the physical properties of ferroelectric thin films. Our approach takes into account the depolarization field and spatial inhomogeneity of the order parameter inherent to thin films. In or approach, we consider the thin film to be short circuited with the perfectly conducting electrodes and monodomain. The solution of the corresponding Euler–Lagrange equation by the direct variational method shows that the initial free-energy functional of a thin film can be reduced to some effective functional which does not include spatial derivatives of the order parameter. The coefficients of this functional, however, are renormalized as compared to those of the initial free-energy functional. We present the detailed calculation of the spontaneous polarization, pyrocoefficient, and dielectric susceptibility. We analyze in detail the spatial profile of the depolarization field with special attention to its properties near size-driven phase transition in a film.

Size effect and evidence of a size-driven phase transition in Bi 4Ti 3O 12 nanocrystals

Bi 4Ti 3O 12 nanocrystals (nc-BTO) were prepared by chemical coprecipitation technique. The crystal structure of the nanocrystals covering mean grain sizes from 16 to 48 nm was determined by X-ray diffraction and refined by the Rietveld method. Differential thermal analysis was employed to investigate the temperature dependent phase transition behavior in nc-BTO. With decreasing grain size the tetragonal–orthorhombic phase transition temperature decreases and ferroelectricity weakens. A size-driven phase transition was found at a critical size d c=44 nm for nc-BTO. The high-temperature tetragonal phase stabilizes at room temperature when d< d c. The origin of the structural anomaly is attributed to higher strain energy induced by lattice strain and to higher inter-phase surface energy difference in nc-BTO system.

Dynamical dielectric susceptibility of ferroelectric thin films and multilayers

The thickness dependence of the real and imaginary parts of the dynamical dielectric susceptibility is investigated phenomenologically for a multilayer structure consisting of alternating ferroelectric and paraelectric layers. It is shown that the frequency dependence of the linear dielectric response can be closely approximated by that of a damped harmonic oscillator, with the static susceptibility, relaxation time, and soft-mode frequency depending on the layer thickness and temperature. When the layer thickness and temperature are equal to their critical values corresponding to the onset of a size-driven ferroelectric phase transition, the static susceptibility and the relaxation time become anomalously large and then decrease with further increasing layer thickness. A spectrum of natural polarization oscillations is predicted to exist with thickness-dependent frequencies. This spectrum includes a soft-mode frequency which vanishes at the critical thickness and at the critical temperature. The frequency spectrum lies below the soft-mode frequency of a thick film (in which the gradient of polarization is negligible). The calculations are compared with experimentally measured dispersion of the dielectric response of a PbTiO3-Pb0.72La0.28TiO3 multilayer structure. The agreement between the theory and experiment is found to be good.

Effects of long-range interactions on the ferroelectric film

The effect of long-range interactions on the spontaneous polarization and the Curie temperature of the ferroelectric film is investigated by use of the Landau theory. On the assumption that the nearest-neighbour interaction remains constant, we find that the spontaneous polarization and the phase transition temperature increase with the enhancement of the long-range interactions. In the case of positive extrapolation length, the critical thickness of the ferroelectric film, in which a size-driven phase transition occurs, decreases with the enhancement of the long-range interactions.

Long-range coupling interactions in ferroelectric sandwich structures

We study the ferroelectric system consisting of the sandwich structure (PbTiO3/BaTiO3/PbTiO3) by using the Ginzburg–Landau phenomenological theory, and emphasize the importance of the long-range coupling interaction to the ferroelectric behavior of the system. We find that after introducing the long-range coupling interaction to the ferroelectric behavior of the sandwich system, the average spontaneous polarization of the interlayer (BaTiO3) increases and a size-driven phase transition disappears. The larger the range of the long-range coupling, the larger the average spontaneous polarization. When the range of the long-range coupling is large enough, the average spontaneous polarization increases gradually with decreasing interlayer thickness, reaches one maximum at a certain finite thickness, and then decreases. The spatial distribution profile of the spontaneous polarization on the range of the coupling interaction for different values of the interlayer thickness is obtained, and the dependence of the averaged polarization on temperature is also examined.

Size-driven phase transition in stress-induced ferroelectric thin films

We have developed a concise phenomenological theory to investigate phase transitions and dielectric properties of ferroelectric thin films under stress. When the polarization at the surface is greater than that in the interior of the film, competition between the ‘superpolarized’ surface and tensile stress leads to a ferroelectric–paraelectric transition above a critical stress. This model is appropriate for the data on stress-induced barium–strontium titanate (BST) thin-film ferroelectric memory devices [Jpn. J. Appl. Phys. 36 (1997) 5846]. Stress–thickness phase diagrams are presented for PbTiO 3 and BaTiO 3 ferroelectric thin films.

Size effects of ferroelectric sandwich structure in the presence of the long-range coupling interaction

We use the Ginzburg-Landau theory to study the ferroelectric system consisting of the sandwich structure (PbTiC3/BaTiC3/PbTiC3). We find that after introducing the long-range coupling interaction, the average spontaneous polarization of the interlayer (BaTiO3) increases and the size-driven phase transition does not occur. The larger the range of the long-range coupling, the larger the average spontaneous polarization. When the range of the long-range coupling is enough large, the average spontaneous polarization increases gradually with decreasing the interlayer thickness, reaches one maximum at a certain finite thickness, and then decreases.