A tetragonal-to-monoclinic phase transition in a ferroelectric perovskite: the structure of PbZr(0.52)Ti(0.48)O3

The perovskite-like ferroelectric system PbZr(1-x)Ti(x)O3 (PZT) has a nearly vertical morphotropic phase boundary (MPB) around x=0.45-0.50. Recent synchrotron x-ray powder diffraction measurements by Noheda et al. [Appl. Phys. Lett. 74, 2059 (1999)] have revealed a new monoclinic phase between the previously-established tetragonal and rhombohedral regions. In the present work we describe a Rietveld analysis of the detailed structure of the tetragonal and monoclinic PZT phases on a sample with x= 0.48 for which the lattice parameters are respectively: at= 4.044 A, ct= 4.138 A, at 325 K, and am= 5.721 A, bm= 5.708 A, cm= 4.138 A, beta= 90.496 deg., at 20K. In the tetragonal phase the shifts of the atoms along the polar [001] direction are similar to those in PbTiO3 but the refinement indicates that there are, in addition, local disordered shifts of the Pb atoms of ~0.2 A perpendicular to the polar axis.. The monoclinic structure can be viewed as a condensation along one of the directions of the local displacements present in the tetragonal phase. It equally well corresponds to a freezing-out of the local displacements along one of the directions recently reported by Corker et al.[J. Phys. Condens. Matter 10, 6251 (1998)] for rhombohedral PZT. The monoclinic structure therefore provides a microscopic picture of the MPB region in which one of the "locally" monoclinic phases in the "average" rhombohedral or tetragonal structures freezes out, and thus represents a bridge between these two phases.Comment: REVTeX, 7 figures. Modifications after referee's suggestion: new figure (figure 5), comments in 2nd para. (Sect.III) and in 2nd & 3rd para. (Sect. IV-a), in the abstract: "...of ~0.2 A perpendicular to the polar axis.

A Raman Study of Morphotropic Phase Boundary in PbZr1-xTixO3 at low temperatures

Raman spectra of PbZr1-xTixO3 ceramics with titanium concentration varying between 0.40 and 0.60 were measured at 7 K. By observing the concentration-frequency dependence of vibrational modes, we identified the boundaries among rhombohedral, monoclinic, and tetragonal ferroelectric phases. The analysis of the spectra was made in the view of theory group analysis making possible the assignment of some modes for the monoclinic phase.Comment: 5 pages, 4 figure

Evidence for MBM_B and MCM_C phases in the morphotropic phase boundary region of (1−x)[Pb(Mg1/3Nb2/3)O3]−xPbTiO3(1-x)[Pb(Mg_{1/3}Nb_{2/3})O_3]-xPbTiO_3 : A Rietveld study

We present here the results of the room temperature dielectric constant measurements and Rietveld analysis of the powder x-ray diffraction data on $(1-x)[Pb(Mg_{1/3}Nb_{2/3})O_3]-xPbTiO_3$(PMN-$x$PT) in the composition range $0.20 \leq x \leq 0.45$ to show that the morphotropic phase boundary (MPB) region contains two monoclinic phases with space groups Cm (or $M_B$ type) and Pm (or $M_C$ type) stable in the composition ranges $0.27 \leq x \leq 0.30$ and $0.31 \leq x \leq 0.34$, respectively. The structure of PMN-$x$PT in the composition ranges $0 \leq x \leq$ 0.26, and $0.35 \leq x \leq1$ is found to be rhombohedral (R3m) and tetragonal (P4mm), respectively. These results are compared with the predictions of Vanderbilt & Cohen's theory.Comment: 20 pages, 11 pdf figure

Phase diagram of the ferroelectric-relaxor (1-x)PbMg(1/3)Nb(2/3)O3-xPbTiO3

Synchrotron x-ray powder diffraction measurements have been performed on unpoled ceramic samples of (1-x)PbMg(1/3)Nb(2/3)O3-xPbTiO3 (PMN-xPT) with 30%<= x<= 39% as a function of temperature around the morphotropic phase boundary (MPB), which is the line separating the rhombohedral and tetragonal phases in the phase diagram. The experiments have revealed very interesting features previously unknown in this or related systems. The sharp and well-defined diffraction profiles observed at high and intermediate temperatures in the cubic and tetragonal phases, respectively, are in contrast to the broad features encountered at low temperatures. These peculiar characteristics, which are associated with the monoclinic phase of MC-type previously reported by Kiat et al and Singh et al., can only be interpreted as multiple coexisting structures with MC as the major component. An analysis of the diffraction profiles has allowed us to properly characterize the PMN-xPT phase diagram and to determine the stability region of the monoclinic phase, which extends from x= 31% to x= 37% at 20 K. The complex lansdcape of observed phases points to an energy balance between the different PMN-xPT phases which is intrinsically much more delicate than that of related systems such as PbZr(1-x)TixO3 or (1-x)PbZn(1/3)Nb(1/3)O3-xPbTiO3. These observations are in good accord with an optical study of x= 33% by Xu et al., who observed monoclinic domains with several different polar directions coexisting with rhombohedral domains, in the same single crystal.Comment: REVTeX4, 11 pages, 10 figures embedde

The challenges of intersectionality: Researching difference in physical education

Researching the intersection of class, race, gender, sexuality and disability raises many issues for educational research. Indeed, Maynard (2002, 33) has recently argued that ‘difference is one of the most significant, yet unresolved, issues for feminist and social thinking at the beginning of the twentieth century’. This paper reviews some of the key imperatives of working with ‘intersectional theory’ and explores the extent to these debates are informing research around difference in education and Physical Education (PE). The first part of the paper highlights some key issues in theorising and researching intersectionality before moving on to consider how difference has been addressed within PE. The paper then considers three ongoing challenges of intersectionality – bodies and embodiment, politics and practice and empirical research. The paper argues for a continued focus on the specific context of PE within education for its contribution to these questions

Stability of the monoclinic phase in the ferroelectric perovskite PbZr(1-x)TixO3

Recent structural studies of ferroelectric PbZr(1-x)TixO3 (PZT) with x= 0.48, have revealed a new monoclinic phase in the vicinity of the morphotropic phase boundary (MPB), previously regarded as the the boundary separating the rhombohedral and tetragonal regions of the PZT phase diagram. In the present paper, the stability region of all three phases has been established from high resolution synchrotron x-ray powder diffraction measurements on a series of highly homogeneous samples with 0.42 <=x<= 0.52. At 20K the monoclinic phase is stable in the range 0.46 <=x<= 0.51, and this range narrows as the temperature is increased. A first-order phase transition from tetragonal to rhombohedral symmetry is observed only for x= 0.45. The MPB, therefore, corresponds not to the tetragonal-rhombohedral phase boundary, but instead to the boundary between the tetragonal and monoclinic phases for 0.46 <=x<= 0.51. This result provides important insight into the close relationship between the monoclinic phase and the striking piezoelectric properties of PZT; in particular, investigations of poled samples have shown that the monoclinic distortion is the origin of the unusually high piezoelectric response of PZT.Comment: REVTeX file, 7 figures embedde

Structure-property relationships in new nonlinear optical borates

SIGLEAvailable from British Library Document Supply Centre-DSC:D193126 / BLDSC - British Library Document Supply CentreGBUnited Kingdo