Neutron and X-ray diffraction study of cubic [111] field cooled Pb(Mg1/3Nb2/3)O3

Neutron and x-ray diffraction techniques have been used to study the competing long and short-range polar order in the relaxor ferroelectric Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) under a [111] applied electric field. Despite reports of a structural transition from a cubic phase to a rhombohedral phase for fields E $>$ 1.7 kV/cm, we find that the bulk unit cell remains cubic (within a sensitivity of 90$^{\circ}$-$\alpha$ =0.03$^{\circ}$)for fields up to 8 kV/cm. Furthermore, we observe a structural transition confined to the near surface volume or `skin' of the crystal where the cubic cell is transformed to a rhombohedral unit cell at T$_{c}$=210 K for E $>$ 4 kV/cm, for which 90$^{\circ}$-$\alpha$=0.08 $\pm$ 0.03$^{\circ}$ below 50 K. While the bulk unit cell remains cubic, a suppression of the diffuse scattering and concomitant enhancement of the Bragg peak intensity is observed below T$_{c}$=210 K, indicating a more ordered structure with increasing electric field yet an absence of a long-range ferroelectric ground state in the bulk. The electric field strength has little effect on the diffuse scattering above T$_{c}$, however below T$_{c}$ the diffuse scattering is reduced in intensity and adopts an asymmetric lineshape in reciprocal space. The absence of hysteresis in our neutron measurements (on the bulk) and the presence of two distinct temperature scales suggests that the ground state of PMN is not a frozen glassy phase as suggested by some theories but is better understood in terms of random fields introduced through the presence of structural disorder. Based on these results, we also suggest that PMN represents an extreme example of the two-length scale problem, and that the presence of a distinct skin maybe necessary for a relaxor ground state.Comment: 12 pages, 9 figure

Structural phase transition and dielectric relaxation in Pb(Zn1/3Nb2/3)O3 single crystals

The structure and the dielectric properties of Pb(Zn1/3Nb2/3)O3 (PZN) crystal have been investigated by means of high-resolution synchrotron x-ray diffraction (with an x-ray energy of 32 keV) and dielectric spectroscopy (in the frequency range of 100 Hz - 1 MHz). At high temperatures, the PZN crystal exhibits a cubic symmetry and polar nanoregions inherent to relaxor ferroelectrics are present, as evidenced by the single (222) Bragg peak and by the noticeable tails at the basis of the peak. At low temperatures, in addition to the well-known rhombohedral phase, another low-symmetry, probably ferroelectric, phase is found. The two phases coexist in the form of mesoscopic domains. The para- to ferroelectric phase transition is diffused and observed between 325 and 390 K, where the concentration of the low-temperature phases gradually increases and the cubic phase disappears upon cooling. However, no dielectric anomalies can be detected in the temperature range of diffuse phase transition. The temperature dependence of the dielectric constant show the maximum at higher temperature (Tm = 417 - 429 K, depending on frequency) with the typical relaxor dispersion at T < Tm and the frequency dependence of Tm fitted to the Vogel-Fulcher relation. Application of an electric field upon cooling from the cubic phase or poling the crystal in the ferroelectric phase gives rise to a sharp anomaly of the dielectric constant at T 390 K and diminishes greatly the dispersion at lower temperatures, but the dielectric relaxation process around Tm remains qualitatively unchanged. The results are discussed in the framework of the present models of relaxors and in comparison with the prototypical relaxor ferroelectric Pb(Mg1/3Nb2/3)O3.Comment: PDF file, 13 pages, 6 figures collected on pp.12-1

Direct observation of the formation of polar nanoregions in Pb(Mg1/3_{1/3}Nb2/3_{2/3})O3_3 using neutron pair distribution function analysis

Using neutron pair distribution function (PDF) analysis over the temperature range from 1000 K to 15 K, we demonstrate the existence of local polarization and the formation of medium-range, polar nanoregions (PNRs) with local rhombohedral order in a prototypical relaxor ferroelectric Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$. We estimate the volume fraction of the PNRs as a function of temperature and show that this fraction steadily increases from 0 % to a maximum of $\sim$ 30% as the temperature decreases from 650 K to 15 K. Below T$\sim$200 K the PNRs start to overlap as their volume fraction reaches the percolation threshold. We propose that percolating PNRs and their concomitant overlap play a significant role in the relaxor behavior of Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$.Comment: 4 pages, 3 figure

Development of Ferroelectric Order in Relaxor (1-x)Pb(Mg1/3Nb2/3)O3 - xPbTiO3

The microstructure and phase transition in relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 (PMN) and its solid solution with PbTiO3 (PT), PMN-xPT, remain to be one of the most puzzling issues of solid state science. In the present work we have investigated the evolution of the phase symmetry in PMN-xPT ceramics as a function of temperature (20 K < T < 500 K) and composition (0 <= x <= 0.15) by means of high-resolution synchrotron x-ray diffraction. Structural analysis based on the experimental data reveals that the substitution of Ti^4+ for the complex B-site (Mg1/3Nb2/3)^4+ ions results in the development of a clean rhombohedral phase at a PT-concentration as low as 5%. The results provide some new insight into the development of the ferroelectric order in PMN-PT, which has been discussed in light of the kinetics of polar nanoregions and the physical models of the relaxor ferroelectrics to illustrate the structural evolution from a relaxor to a ferroelectric state.Comment: Revised version with updated references; 9 pages, 4 figures embedde

Computational modelling of full interaction between crystal plasticity and oxygen diffusion at a crack tip

Oxidation-promoted crack growth, one of the major concerns for nickel-based superalloys, is closely linked to the diffusion of oxygen into the crack tip. The phenomenon is still not well understood yet, especially the full interaction between oxygen diffusion and severe near-tip mechanical deformation. This work aimed at the development of a robust numerical strategy to model the full coupling of crystal plasticity and oxygen diffusion in a single crystal nickel-based superalloy. In order to accomplish this, finite element package ABAQUS is used as a platform to develop a series of user-defined subroutines to model the fully coupled process of deformation and diffusion. The formulation allowed easy incorporation of nonlinear material behaviour, various loading conditions and arbitrary model geometries. Using this method, finite element analyses of oxygen diffusion, coupled with crystal plastic deformation, were carried out to simulate oxygen penetration at a crack tip and associated change of near-tip stress field, which has significance in understanding crack growth acceleration in oxidation environment. Based on fully coupled diffusion-deformation analyses, a case study was carried out to predict crack growth rate in oxidation environment and under dwell-fatigue loading conditions, for which a two-parameter failure criterion, in terms of accumulated inelastic strain and oxygen concentration at the crack tip, has been utilized

Easy induction of a ferroelectric fourfold monoclinic domain state from a tetragonal ferroelectric monodomain state in PbZn1/3Nb 2/3O3

We report a combined pyroelectric, dielectic and structural characterization of PZN single crystals in field cooling (FC) run along [001]. The pyroelectric current and the dielectric permittivity show a new characteristic temperature, at T approximate to 370 K, related to a macroscopic competition between two induced ferroelectric tetragonal (T) and monoclinic (M) phases. The phase transition, which starts around TC-R = 385 K, spreads over a large temperature range and some amount of T-phase is still observed at room temperature (RT). The M-T phase mixture, induced below TC-R, is stable after field removal. According to a previous Raman scattering work, a fourfold symmetry of M-domains is proposed; the residual T-phase is stabilized by the coexistence of four symmetry-allowed M-domains arranged around[001]. Our results confirm that in a restricted temperature range (TC-R - 20 K, TC-R + 20 K) the free energy of the relaxor-ferroelectric PZN is almost independent of the direction of polarization and accordingly the material can switch from one polar order to the other

Kinetic study of PZN single crystal polarization under a static electric field

International audienceA kinetic effect is evidenced in lead zinc niobate (PZN). We measured the time dependencies of the polarisation P(t) of a single crystal. At a given temperature and electric field, P(t) is described by the expression P(t) = P∞(T) f(t/τ(E,T)) where τ(E,T) is the incubation time above which the sample is completely polarised. The τ(E,T) was fitted using the exponential law exp[(W+kδT/E)/kT] where the activation energy W is equal to 0.91±0.36 eV and δT is equal to 2.2×108 K V/m in the 300-360 K temperature range. Taking into account this kinetic effect the electric-field-temperature diagram and the existence of an electric field threshold were discussed

Tetragonal and rhombohedral induced polar order from the relaxor state of PbZn1/3Nb2/3O3

International audienceStructural and dielectric characterizations of the relaxor ferroelectric PbZn1/3Nb2/3 (PZN) were carried out on single crystals in the temperature range of the dielectric anomaly (370 K andlt; T andlt; 440 K), under dc electric field applied along [001]- and [111]-directions. Two ferroelectric phases, tetragonal (T) and rhombohedral (R), can be field induced in this temperature range, the symmetry of which depends on the direction of the applied field. [001] and [111] respectively. E-T diagrams were built and interpreted under the consideration of polar nano-regions (PNRs) with a prominent tetragonal component. These PNRs prevent the onset of a monodomain state when the field is applied along [111] and explain the features of PZN for an applied field along [001] large lattice strain, easy onset of the T phase and suppression of the dielectric relaxation for E ≥ 1.5 kV cm-1. The microscopic origin of these PNRs can be discussed in relation with recent nuclear magnetic resonance and structural results reported in other isomorphous relaxors