Heat capacity study of relaxor PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript> in a wide temperature range

Heat capacity of the PbMg_1/3Nb_2/3O₃ compound is measured using the methods of adiabatic and differential scanning calorimetry in the temperature range 80–750 K. Two blurred anomalies on the C _p (T) dependence are observed in wide temperature intervals of 200–400 K and 500–700 K. The results of studies are discussed together with data on the structure and phonon spectrum in the framework of spherical random bond-random field model.     

Acoustic emission and thermal expansion of Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> and Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript>-PbTiO<Subscript>3</Subscript> crystals

The temperature dependence of the elongation per unit length for Pb(Mg_1/3Nb_2/3)O₃ crystals unannealed after growth and mechanical treatment is investigated in the course of thermocycling. It is revealed that this dependence deviates from linear behavior at temperatures below 350°C. The observed deviation is characteristic of relaxors, is very small in the first cycle, increases with increasing number n of thermocycles, and reaches saturation at n≥3. In the first cycle, a narrow maximum of the acoustic emission activity is observed in the vicinity of 350°C. In the course of thermocycling, the intensity of this maximum decreases and becomes zero at n>3. For (1?x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ crystals, the dependence of the temperature of this acoustic emission maximum on x exhibits a minimum. It is assumed that the phenomena observed are associated with the phase strain hardening due to local phase transitions occurring in compositionally ordered and polar nanoregions.     

A comparative Raman study of 0.65(PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>) -0.35(PbTiO<Subscript>3</Subscript>) single crystal and thin film

We report a comparative Raman study of 0.65(PbMg_1/3Nb_2/3O₃)-0.35(PbTiO₃) (PMN-0.35PT) single crystal and thin film. Raman spectra investigation indicates a change in bulk from the high temperature cubic to the tetragonal phase and then to the low temperature Mc monoclinic phase. The transition temperatures are in good agreement with the ones previously observed by dielectric measurements on the same sample. In contrast, we observe no phase transition to the monoclinic phase in the PMN-0.35PT 4000 Å thick film and only a cubic to tetragonal diffuse transition has been determined at high temperature. The enhanced stability of the tetragonal phase and the absence of low temperature monoclinic phase have been attributed to the in plane strain.     

Dielectric dispersion and magnetic properties of Ba-modified Pb(Fe<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>)O<Subscript>3</Subscript>

The polycrystalline samples of Ba-modified Pb(Fe_1/2Nb_1/2)O₃ (i.e., (Pb_1-xBa_x)(Fe_1/2Nb_1/2)O₃ PBFN, with x=0,0.05,0.07) were synthesized by a mechanosynthesis (i.e., high-energy ball milling) route followed by a mixed oxide method. Structural analysis provides the information on formation of single-phase orthorhombic structure on substitution of a small amount (x=0.07) of Ba at the Pb-site of Pb(Fe_0.50Nb_0.50)O₃ (PFN). The ferroelectric–paraelectric phase transition in PFN was observed at 383 K, which decreases on increasing Ba-concentration in PBFN. Detailed studies of dielectric properties of PBFW show the following: (i) diffuse phase transition, (ii) low loss tangent, (iii) low activation energy, and (iv) low frequency dielectric dispersion. An anomaly in the ac conductivity was found very close to phase transition temperature. The activation energy is found to decrease from 0.19 to 0.01 eV on increasing Ba-concentration to 7% (x=0.07). Temperature field-dependent magnetization measurements of all the samples showed antiferromagnetic transition at ∼15 K (for x=0.07). PBFN sample showed a slight increase in the coercivity (i.e., from 400 Oe (PFN) to 500 Oe (PBFN, for x=0.07) at 2 K. PACS 61.10.Nz; 68.37.Hk; 75.50.Ss; 75.60.Ej; 77.22.Ch; 77.22.Gm     

Optical investigations of structural phase transformations in PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>-<Emphasis Type="Italic">x</Emphasis>PbTiO<Subscript>3</Subscript> single crystals located at the morphotropic phase boundary

A study has been made of the effect of a dc electric field (0 < E < 4 kV/cm) on the optical transmittance of single-crystal compounds PbMg_1/3Nb_2/3O₃-xPbTiO₃ (PMN-xPT) located at the boundaries of the morphotropic region (x = 32.0 and 36.5%) and directly at the center of the morphotropic region (x = 35%). It is shown that, at temperatures close to the morphotropic phase transition point, the electric field induces two phase transitions in PMN-32PT and PMN-35PT crystals and only one phase transition in PMN-36.5PT. The tetragonal (T) phase induced in all three compounds remains stable after the electric field is removed only in crystals with x = 35.0 and 36.5%, whereas the T phase is metastable and transforms into the monoclinic M _c phase after the field is switched off in the PMN-32PT crystals lying at the boundary of the morphotropic region on the rhombohedral side. It is found that the electric-field-induced intermediate phase M _c in PMN-35PT is inhomogeneous and that M _c transforms into the tetragonal phase in a continuous transition. It is suggested that only the presence of a third orthorhombic phase can account for the continuous character of the transition between the M _c and T phases in PMN-35PT crystals. The results obtained are interpreted in terms of the Devonshire theory for strongly anharmonic crystals. The E-T phase diagrams are constructed for all the crystals.     

Heterophase states in 0.10PbTiO<Subscript>3</Subscript>-0.90Pb(Zn<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> crystals

A new model of the elastic matching of phases is proposed, and heterophase structures near the morphotropic phase boundary in 0.10PbTiO₃-0.90Pb(Zn_1/3Nb_2/3)O₃ crystals are studied. Unique behavior of the unit cell parameters is found to favor the elastic matching of the ferroelectric tetragonal and orthorhombic phases under the conditions of complete or partial relaxation of internal mechanical stresses at a volume concentration ratio of these phases of about 20/80% and temperatures of T=20–300 K. Interrelations between the volume concentrations of different domain (twin) types and of the coexisting phases are analyzed.     

Statistical mechanics of cation ordering in PbSc<Subscript>1/2</Subscript>Ta<Subscript>1/2</Subscript>O<Subscript>3</Subscript> and PbSc<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> solid solutions

A model Hamiltonian for B cation ordering (Sc-Nb(Ta)) in PbSc_1/2Nb_1/2O₃ and PbSc_1/2Ta_1/2O₃ solid solutions is constructed. The parameters of the model Hamiltonian are determined from the ab initio calculation within the ionic crystal model with allowance made for the deformability and the dipole and quadrupole polarizabilities of the ions. The temperatures of the phase transition due to the ordering of the B cations are calculated by the Monte Carlo method in the mean-field and cluster approximations. The phase transition temperatures calculated by the Monte Carlo method (1920 K for PbSc_1/2Ta_1/2O₃ and 1810 K for PbSc_1/2Nb_1/2O₃) are consistent with the experimental data (1770 and 1450 K, respectively). The thermodynamic properties of the cation ordering are investigated using the Monte Carlo method.     

Effect of the la concentration on the dielectric and optical properties of the transparent ferroelectric ceramics 75PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>-25PbTiO<Subscript>3</Subscript>

The dielectric, optical, and electro-optical properties of transparent ferroelectric ceramics 75PbMg_1/3Nb_2/3O₃-25PbTiO₃ (75PMN-25PT) with different La concentrations (2, 3, and 4 at %) have been studied. It has been shown that all the samples under study undergo a diffuse phase transition, and the degree of diffuseness increases with an increase in the La concentration. The temperature dependences of the optical transmission in different regimes of applying an electric field and the quadratic electro-optical effect have been investigated. It has been found that, at room temperature, the maximum electro-optical effect is observed in the ceramics with a La concentration of 3 at %. This is explained by the fact that the measurement temperature is close to the Vogel-Fulcher temperature at which the minimum electric field is required to induce ferroelectric states from the relaxor phase.     

Ionic displacements and structure of disordered PbFe<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript>

A sequence of structural models of unit cells of complex oxides with perovskite-type structure has been constructed to refine the average structure of PbFe_1/2Nb_1/2O₃ (PFN) at temperatures above the ferroelectric Curie point (T _C ～ 110°C). Owing to the analysis of the probability theory considerations, each model is characterized by only two positional fitting parameters. With the use of the intensities of 95 symmetrically independent X-ray reflections from a PFN single crystal at 160°C, a model with the R factor below 3% (K = 2.44%) was chosen. The ravine method has been used to verify the existence of a single minimum for the R factor with respect to the fitting parameter.     

Study of ferroelectric phase transitions in disordered PbSc<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> and PbSc<Subscript>1/2</Subscript>Ta<Subscript>1/2</Subscript>O<Subscript>3</Subscript> solid solutions

Ferroelectric phase transitions and thermodynamic properties of disordered PbSc_1/2Ta_1/2O₃ and PbSc_1/2Nb_1/2O₃ solid solutions have been investigated by the Monte Carlo method. The parameters of the effective Hamiltonian were calculated within the generalized Gordon-Kim model. The obtained values of the phase-transition temperatures and spontaneous polarization are in satisfactory agreement with the experimental data.     

Lattice dynamics and ferroelectric instability in ordered and disordered PbSc<Subscript>1/2</Subscript>Ta<Subscript>1/2</Subscript>O<Subscript>3</Subscript> and PbSc<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> solid solutions

The dynamic Born charges and the frequency spectra of lattice oscillations in the crystals of ordered and disordered PbSc_1/2Ta_1/2O₃ (PST) and PbSc_1/2Nb_1/2O₃ (PSN) solid solutions have been calculated within the framework of the generalized Gordon-Kim model with allowance for the dipole and quadrupole polarizabilities. The phonon spectra of both compounds contain ferroelectric soft modes. The influence of various interactions on the magnitude of dynamic charges and ferroelectric instability in PSN and PST solid solutions has been studied and it is shown that both these charges and the ferroelectric instability are determined by the competition between long-range dipole-dipole interactions and short-range dipole-charge interactions, the determining role played by the interaction of Nb (Ta) cations and oxygen anions in the Nb-O (Ta-O) bond direction.     

Formation of nanodomain ensembles during polarization reversal in Sr<Subscript>0.61</Subscript>Ba<Subscript>0.39</Subscript>Nb<Subscript>2</Subscript>O<Subscript>6</Subscript>: Ce single crystals

The results of the study of nano- and microdomain structure evolution in single crystals of relaxor ferroelectric strontium barium niobate Sr_0.61Ba_0.39Nb₂O₆ doped by cerium are presented. It was shown that the initial nanodomain structure represents a self-similar three-dimensional maze. The fractal dimension and average period were revealed. It was demonstrated that application of series of alternating electric field pulses makes it possible to produce a single-domain state in the surface layer. The features of the growth and “merging,” as well as the shape of ensembles of isolated nanodomains formed during switching from the single-domain state, were investigated. The formation of the nanodomain ensembles was considered as a result of the self-organized discrete switching controlled by determined nucleation.     

Dielectric and optical properties of Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)<Subscript>0.8</Subscript>Ti<Subscript>0.2</Subscript>O<Subscript>3</Subscript> (PMNT-0.2) ferroelectric relaxor single crystals

The dielectric and optical (optical transmission, small-angle light scattering, birefringence) properties of PMNT-0.2 single crystals and their variation induced by a dc electric field have been studied. The birefringence was found to increase anomalously at the transition from the rhombohedral ferroelectric to the inhomogeneous relaxor phase (the spontaneous ferroelectric transition temperature T_sp). Below T_sp, the dielectric and optical properties were observed to exhibit anomalies originating from reorientation and growth of domains in size. Unlike ferroelectric relaxors of the type of PbB′_1/3B′_2/3O₃ and PbB′_1/2B′_1/2O₃, in PMNT-0.2 neither induction of the ferroelectric phase by an electric field nor thermally stimulated destruction of the ferroelectric state occurs through the percolation mechanism (i.e., they are not accompanied by anomalously narrow maxima in small-angle light scattering). This is attributed to the inhomogeneous structure of the relaxor phase, as a result of which the phase transition does not take place simultaneously in various regions of the crystal.     

Local structure of disordered PbSc<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> in the region of the diffuse tetragonal phase-rhombohedral phase transition

The local structure of the ferroelectric-relaxor PbSc_1/2Nb_1/2O₃ in the temperature range from 550 to 220 K has been investigated using ⁴⁵Sc nuclear magnetic resonance. It has been found that, in the paraelectric phase at temperatures below 550 K, the crystal consists of regions of an ordered elpasolite structure and inclusions of the disordered tetragonal perovskite phase with displacements along directions of the [001] type. The relative weight of the tetragonal structure in the region of the paraelectric phase is approximately equal to 0.28. Below the temperature of the phase transition from the disordered modification to the polar phase, the relative weight of the tetragonal phase decreases with decreasing temperature. The tetragonal structure is replaced by the trigonal polar structure. In a wide temperature range (∼50 K), there exists a heterophase structure that is characteristic of relaxors. Note that the correlation length of displacements in the tetragonal phase should be very small to explain the absence of indications of the existence of this phase in the diffraction data.     

Polarization 1/<Emphasis Type=Italic>f</Emphasis> noise in ferroelectric PbFe<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> with a diffused phase transition

The dispersion of complex permittivity in ferroelectric PbFe_1/2Nb_1/2O₃ with diffused phase transition at frequencies of 20 Hz-10 kHz was studied. Dielectric measurements revealed that polarization 1/f noise occurs in the region of coexistence of polar and nonpolar phases. It was found that the temperature dependence of parameter α exhibits a singularity when the temperature of the local order parameter rises. Our analysis of the experimental data enables us to say that the source of the noise is the fluctuations of spontaneous polarization.     

Polar nanoregions in Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> (PMN): insights from a supercell approach

We report construction of a model of polar nanoregions in the PMN relaxor ferroelectric based on first-principles lattice dynamics for chemically ordered supercells [S.A. Prosandeev et al., Phys. Rev. B 70, 134110 (2004)], combined with invariance under permutations and dipole-dipole interaction as a source supporting randomly oriented residual polarization. Representative analytical estimates of polar nanore-gion — supercell mapping reproduce both nonzero local and zero macroscopic polarization of the structure, as well as the temperature change of the supercell anisotropy at cooling and field cooling.     

Preparation and dielectric properties of the lead-free BaFe<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> ceramics obtained from mechanically triggered powder

In the paper the influence of mechanical activation of the powder on the final dielectric properties lead-free Ba(Fe_1/2Nb_1/2)O₃ (BFN) ceramic was examined. The BFN ceramics were obtained by 3-steps route. Firstly, the substrates were pre-homogenized in a planetary ball mill. Than, the powder was activated in vibratory mill (the shaker type SPEX 8000 Mixer Mill) for different duration between 25 h and 100 h. The influence of the milling time on the BFN powder was monitored by X-ray diffraction. The diffraction data confirmed that the milling process of the starting components is accompanied by partial synthesis of the BFN materials. The longer of the high-energy milling duration the powders results in increasing the amount of amorphous/nanocrystalline content. The mechanically activated materials were sintered in order to obtain the ceramic samples. During this temperature treatment the final crystallisation of the powder appeared what was confirmed by XRD studies. The performed dielectric measurements have revealed the reduction of the dielectric loss of the BFN ceramics compared to materials obtained by classic methods.     

Long-time relaxation phenomena in Pb<Subscript>0.94</Subscript>Ba<Subscript>0.06</Subscript>Sc<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> (PBSN-6) single crystals

Long-time polarization relaxation in the temperature range where PBSN-6 single crystals reside in the relaxor state was studied. An analysis of the time dependence of the permittivity ε′(t) performed at measuring frequencies from 1 Hz to 1 kHz in weak electric fields E₀ showed that the relaxation (or freezing) times derived by extrapolating relations of the type ε′(t) ～ log(t/t₀) and ε′(t) ～ exp{?[ln(t/t₀)]_β} range from 10⁸ to 10¹¹ min and depend substantially on the bias voltage applied to the sample. A study of the pattern of the dielectric response in moderate and strong infralow-frequency fields revealed that, after a sample was maintained under a bias lower than the coercive force, it no longer exhibited the additional anomalies in the amplitude dependences of the effective loss tangent tan_eff(E₀) than were observed in a thermally recuperated sample.